From 50704eba0740282d2d8cbb33118edc02b533ce96 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jean-S=C3=A9bastien?= <git@jscaux.org>
Date: Thu, 24 Mar 2022 08:43:21 +0100
Subject: [PATCH] Update 2022-03-24 08:43

---
 build/a.html                             |    6 +-
 build/a_l.html                           |    6 +-
 build/c.html                             |    6 +-
 build/c_m.html                           |    6 +-
 build/c_m_cs.html                        |    6 +-
 build/c_m_cs_cyl.html                    |   18 +-
 build/c_m_cs_hyp.html                    |    6 +-
 build/c_m_cs_sph.html                    |   38 +-
 build/c_m_dc.html                        |    6 +-
 build/c_m_dc_curl.html                   |    6 +-
 build/c_m_dc_d2.html                     |   40 +-
 build/c_m_dc_del.html                    |    6 +-
 build/c_m_dc_div.html                    |    6 +-
 build/c_m_dc_g.html                      |    6 +-
 build/c_m_dc_pr.html                     |   30 +-
 build/c_m_dd.html                        |    6 +-
 build/c_m_dd_1d.html                     |    6 +-
 build/c_m_dd_3d.html                     |   18 +-
 build/c_m_dd_div.html                    |    6 +-
 build/c_m_ic.html                        |    6 +-
 build/c_m_ic_ftc.html                    |    6 +-
 build/c_m_ic_ftg.html                    |    6 +-
 build/c_m_ic_gauss.html                  |    6 +-
 build/c_m_ic_ip.html                     |    6 +-
 build/c_m_ic_lsv.html                    |   24 +-
 build/c_m_ic_stokes.html                 |   10 +-
 build/c_m_uf.html                        |    6 +-
 build/c_m_uf_cyl.html                    |    6 +-
 build/c_m_uf_sph.html                    |    6 +-
 build/c_m_uf_vi.html                     |    6 +-
 build/c_m_va.html                        |    6 +-
 build/c_m_va_cp.html                     |    6 +-
 build/c_m_va_n.html                      |    6 +-
 build/c_m_va_pds.html                    |    6 +-
 build/c_m_va_sp.html                     |    6 +-
 build/c_m_va_tp.html                     |    6 +-
 build/c_m_vf.html                        |    6 +-
 build/c_m_vf_helm.html                   |    6 +-
 build/c_m_vf_pot.html                    |    6 +-
 build/d.html                             |   10 +-
 build/d_emd.html                         |    6 +-
 build/d_emd_ce.html                      |    6 +-
 build/d_emd_emw.html                     |    6 +-
 build/d_emf.html                         |    6 +-
 build/d_ems.html                         |    6 +-
 build/d_ems_ca.html                      |    6 +-
 build/d_ems_ms.html                      |    6 +-
 build/d_emsm.html                        |    6 +-
 build/d_emsm_msm.html                    |    6 +-
 build/d_m.html                           |    6 +-
 build/d_red.html                         |    6 +-
 build/emd.html                           |   14 +-
 build/emd_Fl.html                        |    6 +-
 build/emd_Fl_Fl.html                     |   28 +-
 build/emd_Fl_e.html                      |   18 +-
 build/emd_Fl_i.html                      |   24 +-
 build/emd_Fl_ief.html                    |   12 +-
 build/emd_Me.html                        |    6 +-
 build/emd_Me_Me.html                     |   20 +-
 build/emd_Me_dc.html                     |   18 +-
 build/emd_Me_ebM.html                    |   10 +-
 build/emd_Me_mc.html                     |    6 +-
 build/emd_ce.html                        |   14 +-
 build/emd_ce_amom.html                   |   12 +-
 build/emd_ce_ce.html                     |    8 +-
 build/emd_ce_mom.html                    |   18 +-
 build/emd_ce_mst.html                    |   24 +-
 build/emd_ce_poy.html                    |   42 +-
 build/emd_emw.html                       |   14 +-
 build/emd_emw_ep.html                    |   14 +-
 build/emd_emw_mpw.html                   |   16 +-
 build/emd_emw_we.html                    |   12 +-
 build/emdm.html                          |    6 +-
 build/emdm_Me.html                       |    6 +-
 build/emdm_Me_Mem.html                   |   42 +-
 build/emdm_Me_bc.html                    |   38 +-
 build/emdm_emwm.html                     |   14 +-
 build/emdm_emwm_ad.html                  |    6 +-
 build/emdm_emwm_ad_c.html                |    6 +-
 build/emdm_emwm_plm.html                 |   18 +-
 build/emdm_emwm_refl.html                |    6 +-
 build/emdm_emwm_refl_ni.html             |   10 +-
 build/emdm_emwm_refl_oi.html             |   30 +-
 build/emdm_emwm_refr.html                |    6 +-
 build/emdm_emwm_wg.html                  |    6 +-
 build/emdm_emwm_wg_c.html                |    6 +-
 build/emdm_emwm_wg_gw.html               |    6 +-
 build/emdm_emwm_wg_r.html                |    6 +-
 build/emf.html                           |   14 +-
 build/emf_g.html                         |    6 +-
 build/emf_g_Cg.html                      |    6 +-
 build/emf_g_Lg.html                      |   30 +-
 build/emf_svp.html                       |   26 +-
 build/ems.html                           |    6 +-
 build/ems_ca.html                        |   14 +-
 build/ems_ca_fe.html                     |   14 +-
 build/ems_ca_fe_L.html                   |   40 +-
 build/ems_ca_fe_g.html                   |   18 +-
 build/ems_ca_fe_uP.html                  |   22 +-
 build/ems_ca_me.html                     |    6 +-
 build/ems_ca_me_Ed.html                  |   14 +-
 build/ems_ca_me_Eq.html                  |    6 +-
 build/ems_ca_me_a.html                   |   22 +-
 build/ems_ca_me_h.html                   |   26 +-
 build/ems_ca_me_md.html                  |   18 +-
 build/ems_ca_mi.html                     |   10 +-
 build/ems_ca_mi_fe.html                  |   10 +-
 build/ems_ca_mi_isc.html                 |   14 +-
 build/ems_ca_mi_o.html                   |    6 +-
 build/ems_ca_sv.html                     |    6 +-
 build/ems_ca_sv_car.html                 |   30 +-
 build/ems_ca_sv_cyl.html                 |    6 +-
 build/ems_ca_sv_sph.html                 |   64 +-
 build/ems_es.html                        |   14 +-
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 build/ems_es_c_cap.html                  |    8 +-
 build/ems_es_c_ic.html                   |    8 +-
 build/ems_es_c_p.html                    |    8 +-
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 build/ems_es_ec.html                     |    6 +-
 build/ems_es_ec_b.html                   |    6 +-
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 build/ems_es_ec_q.html                   |    6 +-
 build/ems_es_ec_s.html                   |    6 +-
 build/ems_es_ef.html                     |    6 +-
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 build/ems_es_ef_ccd.html                 |   28 +-
 build/ems_es_ef_pc.html                  |   20 +-
 build/ems_es_efo.html                    |    6 +-
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 build/ems_es_efo_e.html                  |   10 +-
 build/ems_es_efo_exp.html                |   22 +-
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 build/ems_es_ep_bc.html                  |   14 +-
 build/ems_es_ep_d.html                   |   46 +-
 build/ems_es_ep_ex.html                  |   10 +-
 build/ems_es_ep_fp.html                  |   12 +-
 build/ems_ms.html                        |   14 +-
 build/ems_ms_BS.html                     |   30 +-
 build/ems_ms_ce.html                     |   12 +-
 build/ems_ms_dcB.html                    |    6 +-
 build/ems_ms_dcB_c.html                  |   34 +-
 build/ems_ms_dcB_d.html                  |   12 +-
 build/ems_ms_dcB_iw.html                 |   10 +-
 build/ems_ms_lf.html                     |    6 +-
 build/ems_ms_lf_pc.html                  |   16 +-
 build/ems_ms_lf_sc.html                  |   32 +-
 build/ems_ms_vp.html                     |    6 +-
 build/ems_ms_vp_A.html                   |   42 +-
 build/ems_ms_vp_LC.html                  |   20 +-
 build/ems_ms_vp_comp.html                |    6 +-
 build/ems_ms_vp_mbc.html                 |   24 +-
 build/ems_ms_vp_me.html                  |   34 +-
 build/emsm.html                          |   14 +-
 build/emsm_esm.html                      |    6 +-
 build/emsm_esm_D.html                    |   32 +-
 build/emsm_esm_D_bc.html                 |   16 +-
 build/emsm_esm_di.html                   |    8 +-
 build/emsm_esm_ld.html                   |    6 +-
 build/emsm_esm_ld_bvp.html               |   32 +-
 build/emsm_esm_ld_e.html                 |   12 +-
 build/emsm_esm_ld_f.html                 |   14 +-
 build/emsm_esm_ld_sp.html                |   26 +-
 build/emsm_esm_mE.html                   |    6 +-
 build/emsm_esm_mE_P.html                 |    6 +-
 build/emsm_esm_mE_o.html                 |   22 +-
 build/emsm_esm_po.html                   |   30 +-
 build/emsm_esm_po_fid.html               |   16 +-
 build/emsm_esm_po_pibc.html              |    6 +-
 build/emsm_msm.html                      |   14 +-
 build/emsm_msm_H.html                    |    6 +-
 build/emsm_msm_H_A.html                  |   50 +-
 build/emsm_msm_a.html                    |    6 +-
 build/emsm_msm_fmo.html                  |    6 +-
 build/emsm_msm_fmo_bc.html               |   26 +-
 build/emsm_msm_fmo_fim.html              |    6 +-
 build/emsm_msm_fmo_pibc.html             |    6 +-
 build/emsm_msm_lnlm.html                 |    6 +-
 build/emsm_msm_lnlm_fm.html              |    6 +-
 build/emsm_msm_lnlm_sp.html              |   24 +-
 build/emsm_msm_m.html                    |    6 +-
 build/emsm_msm_m_dpf.html                |   12 +-
 build/emsm_msm_m_fdi.html                |   18 +-
 build/fig/red/red_motion_under_cst_F.asy |    4 +-
 build/fig/red/red_motion_under_cst_F.svg |  142 +-
 build/in.html                            |    6 +-
 build/in_p.html                          |    6 +-
 build/in_t.html                          |    6 +-
 build/in_t_c.html                        |   34 +-
 build/in_t_l.html                        |    6 +-
 build/index.html                         |    8 +-
 build/qed.html                           |   12 +-
 build/qed_t.html                         | 1641 ----------------------
 build/red.html                           |   14 +-
 build/red_rem.html                       |    6 +-
 build/red_rem_Fmunu.html                 |   32 +-
 build/red_rem_Ltf.html                   |   32 +-
 build/red_rem_Me.html                    |   46 +-
 build/red_rem_mre.html                   |    8 +-
 build/red_rm.html                        |    6 +-
 build/red_rm_Mf.html                     |   24 +-
 build/red_rm_pt.html                     |   10 +-
 build/red_rm_rme.html                    |   14 +-
 build/red_sr.html                        |    6 +-
 build/red_sr_4v.html                     |   12 +-
 build/red_sr_Lt.html                     |    8 +-
 build/red_sr_p.html                      |   14 +-
 211 files changed, 1506 insertions(+), 3143 deletions(-)
 delete mode 100644 build/qed_t.html

diff --git a/build/a.html b/build/a.html
index 9466867..0349b6a 100644
--- a/build/a.html
+++ b/build/a.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/a_l.html b/build/a_l.html
index 88cb9b4..e77b5ac 100644
--- a/build/a_l.html
+++ b/build/a_l.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1720,7 +1720,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c.html b/build/c.html
index c78b680..6f5b37e 100644
--- a/build/c.html
+++ b/build/c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m.html b/build/c_m.html
index f767f07..4909033 100644
--- a/build/c_m.html
+++ b/build/c_m.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_cs.html b/build/c_m_cs.html
index 883f7f2..e092e3c 100644
--- a/build/c_m_cs.html
+++ b/build/c_m_cs.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_cs_cyl.html b/build/c_m_cs_cyl.html
index 9e9c0e6..bd3f671 100644
--- a/build/c_m_cs_cyl.html
+++ b/build/c_m_cs_cyl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1659,14 +1659,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
 <div id="outline-container-c_m_cs_cyl_grad" class="outline-6">
 <h6 id="c_m_cs_cyl_grad"><a href="#c_m_cs_cyl_grad">Gradient</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_cyl_grad">
-<div class="eqlabel" id="org699f087">
+<div class="eqlabel" id="org718e42d">
 <p>
 <a id="cylgrad"></a><a href="./c_m_cs_cyl.html#cylgrad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2197539">
+<div class="alteqlabels" id="org9ec66cd">
 <ul class="org-ul">
 <li>Gr4(1.79)</li>
 </ul>
@@ -1687,14 +1687,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
 <div id="outline-container-c_m_cs_cyl_div" class="outline-6">
 <h6 id="c_m_cs_cyl_div"><a href="#c_m_cs_cyl_div">Divergence</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_cyl_div">
-<div class="eqlabel" id="org02508ba">
+<div class="eqlabel" id="orgd5ab218">
 <p>
 <a id="cyl_div"></a><a href="./c_m_cs_cyl.html#cyl_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7c0369d">
+<div class="alteqlabels" id="orgd93619e">
 <ul class="org-ul">
 <li>Gr4(2.21)</li>
 </ul>
@@ -1715,14 +1715,14 @@ Range of parameters:  \(r \in [0, \infty[\), \(\varphi \in [0, 2\pi[\) and \(z \
 <div id="outline-container-c_m_cs_cyl_curl" class="outline-6">
 <h6 id="c_m_cs_cyl_curl"><a href="#c_m_cs_cyl_curl">Curl</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_cyl_curl">
-<div class="eqlabel" id="orgc355dd0">
+<div class="eqlabel" id="orgabcc2d8">
 <p>
 <a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8037114">
+<div class="alteqlabels" id="orga07a427">
 <ul class="org-ul">
 <li>Gr4(2.21)</li>
 </ul>
@@ -1771,7 +1771,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_cs_hyp.html b/build/c_m_cs_hyp.html
index 5e3e1be..6073cc0 100644
--- a/build/c_m_cs_hyp.html
+++ b/build/c_m_cs_hyp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1632,7 +1632,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_cs_sph.html b/build/c_m_cs_sph.html
index e42448c..0c9527f 100644
--- a/build/c_m_cs_sph.html
+++ b/build/c_m_cs_sph.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1623,14 +1623,14 @@ which \(r\) is the distance from the chosen origin,
 The usual Cartesian coordinates relate to spherical coordinates
 according to
 </p>
-<div class="eqlabel" id="org309b2e9">
+<div class="eqlabel" id="org763df52">
 <p>
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-<div class="alteqlabels" id="org7a6a40a">
+<div class="alteqlabels" id="orgb59869b">
 
 </div>
 
@@ -1655,14 +1655,14 @@ A generic vector can be expressed as
 where the explicit relation between spherical and
 Cartesian unit vectors is
 </p>
-<div class="eqlabel" id="org43b8824">
+<div class="eqlabel" id="org923fbbc">
 <p>
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-<div class="alteqlabels" id="org054cde6">
+<div class="alteqlabels" id="org2051229">
 
 </div>
 
@@ -1685,14 +1685,14 @@ and \(\hat{\boldsymbol \varphi} (\theta, \varphi)\).
 <p>
 An infinitesimal displacement \(d{\bf l}\) can be written as
 </p>
-<div class="eqlabel" id="org0afd234">
+<div class="eqlabel" id="orgb032a0d">
 <p>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgce4cca6">
+<div class="alteqlabels" id="orgaeea797">
 
 </div>
 
@@ -1708,14 +1708,14 @@ d{\bf l} = dr ~\hat{\boldsymbol r} + r d\theta ~\hat{\boldsymbol \theta} + r\sin
 <p>
 Infinitesimal volume element:
 </p>
-<div class="eqlabel" id="org260d3f6">
+<div class="eqlabel" id="orgf42297c">
 <p>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org5ac82f0">
+<div class="alteqlabels" id="orgb0160b3">
 
 </div>
 
@@ -1736,14 +1736,14 @@ Infinitesimal surface element:  depends on situation.
 <div id="outline-container-c_m_cs_sph_grad" class="outline-6">
 <h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_sph_grad">
-<div class="eqlabel" id="org0a3cd9b">
+<div class="eqlabel" id="orgbf5f354">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdf69aa8">
+<div class="alteqlabels" id="orgbda0409">
 
 </div>
 
@@ -1760,14 +1760,14 @@ Infinitesimal surface element:  depends on situation.
 <div id="outline-container-c_m_cs_sph_div" class="outline-6">
 <h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_sph_div">
-<div class="eqlabel" id="orgc4833f8">
+<div class="eqlabel" id="orge3c6cf7">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org12f3039">
+<div class="alteqlabels" id="orged88fee">
 
 </div>
 
@@ -1784,14 +1784,14 @@ Infinitesimal surface element:  depends on situation.
 <div id="outline-container-c_m_cs_sph_curl" class="outline-6">
 <h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_sph_curl">
-<div class="eqlabel" id="org6a4b6db">
+<div class="eqlabel" id="org34ae3e4">
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   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org47ac74d">
+<div class="alteqlabels" id="org5f176f6">
 
 </div>
 
@@ -1810,14 +1810,14 @@ Infinitesimal surface element:  depends on situation.
 <div id="outline-container-c_m_cs_sph_lap" class="outline-6">
 <h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
 <div class="outline-text-6" id="text-c_m_cs_sph_lap">
-<div class="eqlabel" id="orgb7a43f7">
+<div class="eqlabel" id="orgb40c79b">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgcba73ed">
+<div class="alteqlabels" id="org1c581f6">
 
 </div>
 
@@ -1851,7 +1851,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc.html b/build/c_m_dc.html
index 17a790f..8a9c717 100644
--- a/build/c_m_dc.html
+++ b/build/c_m_dc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1642,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_curl.html b/build/c_m_dc_curl.html
index afc4ed5..b6a92e3 100644
--- a/build/c_m_dc_curl.html
+++ b/build/c_m_dc_curl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1644,7 +1644,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_d2.html b/build/c_m_dc_d2.html
index 08d4287..0f5f299 100644
--- a/build/c_m_dc_d2.html
+++ b/build/c_m_dc_d2.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1615,9 +1615,9 @@ Table of contents
 <div class="outline-text-5" id="text-c_m_dc_d2">
 </div>
 
-<div id="outline-container-org78664e4" class="outline-6">
-<h6 id="org78664e4"><a href="#org78664e4">Divergence of gradient</a></h6>
-<div class="outline-text-6" id="text-org78664e4">
+<div id="outline-container-org873f1bb" class="outline-6">
+<h6 id="org873f1bb"><a href="#org873f1bb">Divergence of gradient</a></h6>
+<div class="outline-text-6" id="text-org873f1bb">
 <p>
 \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
 The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
@@ -1626,44 +1626,44 @@ given by the Laplacian of the corresponding vector elements.
 </div>
 </div>
 
-<div id="outline-container-orgecb53d1" class="outline-6">
-<h6 id="orgecb53d1"><a href="#orgecb53d1">Curl of a gradient</a></h6>
-<div class="outline-text-6" id="text-orgecb53d1">
+<div id="outline-container-orged6374e" class="outline-6">
+<h6 id="orged6374e"><a href="#orged6374e">Curl of a gradient</a></h6>
+<div class="outline-text-6" id="text-orged6374e">
 <p>
 This always vanishes.
 </p>
 </div>
 </div>
 
-<div id="outline-container-orgdeab960" class="outline-6">
-<h6 id="orgdeab960"><a href="#orgdeab960">Gradient of the divergence</a></h6>
-<div class="outline-text-6" id="text-orgdeab960">
+<div id="outline-container-orgcf8bc6c" class="outline-6">
+<h6 id="orgcf8bc6c"><a href="#orgcf8bc6c">Gradient of the divergence</a></h6>
+<div class="outline-text-6" id="text-orgcf8bc6c">
 <p>
 \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics.  No special name.
 </p>
 </div>
 </div>
 
-<div id="outline-container-org11519c8" class="outline-6">
-<h6 id="org11519c8"><a href="#org11519c8">Divergence of a curl</a></h6>
-<div class="outline-text-6" id="text-org11519c8">
+<div id="outline-container-orgc1dc4c7" class="outline-6">
+<h6 id="orgc1dc4c7"><a href="#orgc1dc4c7">Divergence of a curl</a></h6>
+<div class="outline-text-6" id="text-orgc1dc4c7">
 <p>
 This always vanishes.
 </p>
 </div>
 </div>
 
-<div id="outline-container-org8bb99ae" class="outline-6">
-<h6 id="org8bb99ae"><a href="#org8bb99ae">Curl of curl</a></h6>
-<div class="outline-text-6" id="text-org8bb99ae">
-<div class="eqlabel" id="org38dd889">
+<div id="outline-container-org766740d" class="outline-6">
+<h6 id="org766740d"><a href="#org766740d">Curl of curl</a></h6>
+<div class="outline-text-6" id="text-org766740d">
+<div class="eqlabel" id="orga94a832">
 <p>
 <a id="curlcurl"></a><a href="./c_m_dc_d2.html#curlcurl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb8e88ad">
+<div class="alteqlabels" id="orgc3745e4">
 
 </div>
 
@@ -1694,7 +1694,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_del.html b/build/c_m_dc_del.html
index 12b1ffa..9d2ca95 100644
--- a/build/c_m_dc_del.html
+++ b/build/c_m_dc_del.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_div.html b/build/c_m_dc_div.html
index 33e2cf7..9c7b98e 100644
--- a/build/c_m_dc_div.html
+++ b/build/c_m_dc_div.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_g.html b/build/c_m_dc_g.html
index 6816a5c..cb452b0 100644
--- a/build/c_m_dc_g.html
+++ b/build/c_m_dc_g.html
@@ -1,7 +1,7 @@
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 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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@@ -1664,7 +1664,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dc_pr.html b/build/c_m_dc_pr.html
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-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
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@@ -1293,7 +1293,7 @@ Table of contents
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 <ul>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1622,14 +1622,14 @@ explicited as follows:
 <p>
 <b>Gradient of a product</b>:
 </p>
-<div class="eqlabel" id="org89b1475">
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@@ -1649,14 +1649,14 @@ explicited as follows:
 <p>
 <b>Gradient of a scalar product</b>:
 </p>
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@@ -1676,14 +1676,14 @@ explicited as follows:
 <p>
 <b>Divergence of a product</b>:
 </p>
-<div class="eqlabel" id="org16aa48b">
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@@ -1703,14 +1703,14 @@ explicited as follows:
 <p>
 <b>Divergence of a cross product</b>:
 </p>
-<div class="eqlabel" id="orga48567e">
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 <ul class="org-ul">
 <li>Gr (6)</li>
 <li>W (1-116)</li>
@@ -1730,14 +1730,14 @@ explicited as follows:
 <p>
 <b>Curl of a product</b>:
 </p>
-<div class="eqlabel" id="org3dec348">
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@@ -1757,14 +1757,14 @@ explicited as follows:
 <p>
 <b>Curl of a cross product</b>:
 </p>
-<div class="eqlabel" id="orga9f7b57">
+<div class="eqlabel" id="org81448bf">
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@@ -1805,7 +1805,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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diff --git a/build/c_m_dd.html b/build/c_m_dd.html
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-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dd_1d.html b/build/c_m_dd_1d.html
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+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1651,7 +1651,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dd_3d.html b/build/c_m_dd_3d.html
index 6a365a5..b707596 100644
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-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,14 +1636,14 @@ Resolution of divergence of \(\hat{\bf r}/r^2\) paradox:
 More generally,
 </p>
 
-<div class="eqlabel" id="orga7ea793">
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+<div class="alteqlabels" id="orgd295657">
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 <li>Gr (1.100)</li>
 </ul>
@@ -1662,14 +1662,14 @@ More generally,
 Since
 </p>
 
-<div class="eqlabel" id="org0791e6b">
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+<div class="alteqlabels" id="orgd9d8d13">
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 <p>
 we have that
 </p>
-<div class="eqlabel" id="org72632aa">
+<div class="eqlabel" id="org4584082">
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-<div class="alteqlabels" id="orgc9783d9">
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@@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_dd_div.html b/build/c_m_dd_div.html
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 <html lang="en">
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-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_ic.html b/build/c_m_ic.html
index 971b004..f927a34 100644
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 <!DOCTYPE html>
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 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
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@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1642,7 +1642,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_ic_ftc.html b/build/c_m_ic_ftc.html
index 760adf0..461159b 100644
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+<!-- 2022-03-24 Thu 08:42 -->
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 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
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 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_ic_ftg.html b/build/c_m_ic_ftg.html
index 337bbdd..1d66579 100644
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 <meta name="viewport" content="width=device-width, initial-scale=1">
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@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1649,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_ic_gauss.html b/build/c_m_ic_gauss.html
index 0cf78ec..efdda8b 100644
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@@ -1,7 +1,7 @@
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+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
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 <ul>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1643,7 +1643,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/c_m_ic_ip.html b/build/c_m_ic_ip.html
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+<!-- 2022-03-24 Thu 08:42 -->
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@@ -1293,7 +1293,7 @@ Table of contents
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 <p class="validation"></p>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
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 <p class="validation"></p>
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@@ -1293,7 +1293,7 @@ Table of contents
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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 <p class="validation"></p>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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 Objectives
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-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1644,18 +1644,18 @@ Empirically:  the changing magnetic field induces an electric current around
 the circuit. This current is really driven by an electric field having a component
 along the wire.  The line integral of this field is called the
 </p>
-<div class="core div" id="orgc1ab4b8">
+<div class="core div" id="orgb0fd5b4">
 <p>
 <b>Electromotive force (or electromotance)</b>,
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+<div class="alteqlabels" id="org516a196">
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@@ -1680,14 +1680,14 @@ The precise statement associated to Faraday's observations
 is that the electromotive force is proportional
 to the rate of change of the magnetic flux,
 </p>
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@@ -1702,18 +1702,18 @@ to the rate of change of the magnetic flux,
 \]
 so we obtain
 </p>
-<div class="core div" id="org3b354eb">
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 \]
 we obtain
 </p>
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 <a id="Fl"></a><a href="./emd_Fl_Fl.html#Fl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org859ac4a">
+<div class="alteqlabels" id="org6a61522">
 <ul class="org-ul">
 <li>Gr (7.16)</li>
 </ul>
@@ -1790,7 +1790,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Fl_e.html b/build/emd_Fl_e.html
index e02406a..92b168b 100644
--- a/build/emd_Fl_e.html
+++ b/build/emd_Fl_e.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,14 +1639,14 @@ W = \frac{1}{2} I \oint {\bf A} \cdot d{\bf l} = \frac{1}{2} \oint ({\bf A} \cdo
 \]
 Generalization to volume currents:
 </p>
-<div class="eqlabel" id="org3409c0a">
+<div class="eqlabel" id="orge9580af">
 <p>
 <a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org84f1d51">
+<div class="alteqlabels" id="orgbe0c60a">
 <ul class="org-ul">
 <li>Gr (7.31)</li>
 </ul>
@@ -1681,15 +1681,15 @@ W = \frac{1}{2\mu_0} \left[ \int_{\cal V} d\tau B^2 - \int_{\cal V} d\tau {\bold
 \]
 We can integrate over all space:  after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
 </p>
-<div class="core div" id="orgced7757">
-<div class="eqlabel" id="orgd899514">
+<div class="core div" id="org9173f2d">
+<div class="eqlabel" id="org717e156">
 <p>
 <a id="W_intBsq"></a><a href="./emd_Fl_e.html#W_intBsq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf7c92a2">
+<div class="alteqlabels" id="org0d5a0b3">
 <ul class="org-ul">
 <li>Gr (7.34)</li>
 </ul>
@@ -1718,7 +1718,7 @@ W_{mag} &amp;= \frac{1}{2} \int d\tau ~({\bf A} \cdot {\bf J}) &amp;= \frac{1}{2
 which are equations <a href="./ems_es_e.html#W_vcd">W_vcd</a>, <a href="./ems_es_e.html#W_intEsq">W_intEsq</a>, <a href="./emd_Fl_e.html#W_intAJ">W_intAJ</a> and <a href="./emd_Fl_e.html#W_intBsq">W_intBsq</a>.
 </p>
 
-<div class="example div" id="orge558476">
+<div class="example div" id="org34d5a7d">
 <p>
 <b>Example: energy in coaxial cable</b>
 </p>
@@ -1768,7 +1768,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Fl_i.html b/build/emd_Fl_i.html
index 3c1850b..b4eecfd 100644
--- a/build/emd_Fl_i.html
+++ b/build/emd_Fl_i.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1641,14 +1641,14 @@ so
 \]
 and we can write the mutual inductance as the <b>Neumann formula</b>,
 </p>
-<div class="eqlabel" id="org3ec4c18">
+<div class="eqlabel" id="org1f70ff2">
 <p>
 <a id="Newmann_M"></a><a href="./emd_Fl_i.html#Newmann_M"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7ff8d1e">
+<div class="alteqlabels" id="org57de753">
 <ul class="org-ul">
 <li>Gr (7.22)</li>
 </ul>
@@ -1665,14 +1665,14 @@ M_{21} = \frac{\mu_0}{4\pi} \oint_{{\cal P}_1} \oint_{{\cal P}_2} \frac{d{\bf l}
 Two things:
 first, \(M_{21}\) is purely geometrical.  Second,
 </p>
-<div class="eqlabel" id="orge7f5edd">
+<div class="eqlabel" id="org43668cc">
 <p>
 <a id="Msym"></a><a href="./emd_Fl_i.html#Msym"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org54ddc77">
+<div class="alteqlabels" id="org7b1e4fa">
 <ul class="org-ul">
 <li>Gr (7.23)</li>
 </ul>
@@ -1687,7 +1687,7 @@ M_{12} = M_{21}
 \]
 </p>
 
-<div class="example div" id="org1bcebe3">
+<div class="example div" id="orgecf7176">
 <p>
 <b>Example: solenoid in solenoid</b>
 </p>
@@ -1735,14 +1735,14 @@ What if we vary current in loop 1?  Flux in 2 will vary.  Induces EMF in loop 2:
 \]
 Changing current also induces EMF in the source loop itself:
 </p>
-<div class="eqlabel" id="orgdaaac4e">
+<div class="eqlabel" id="org2512f69">
 <p>
 <a id="PLI"></a><a href="./emd_Fl_i.html#PLI"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb8faf94">
+<div class="alteqlabels" id="org080d683">
 <ul class="org-ul">
 <li>Gr (7.25)</li>
 </ul>
@@ -1765,7 +1765,7 @@ Inductance:  measured in <b>henries</b> (\(H\)).  \(H = V s/A\).
 </p>
 
 
-<div class="example div" id="org11544ba">
+<div class="example div" id="orgce99b7c">
 <p>
 <b>Example: self-inductance of toroidal coil</b>
 </p>
@@ -1804,7 +1804,7 @@ Inductance (like capacitance) is intrinsically positive.  Use Lenz law.
 Think of <i>back EMF</i>.
 </p>
 
-<div class="example div" id="org52373ca">
+<div class="example div" id="orgb4d543b">
 <p>
 <b>Example: circuit</b>
 </p>
@@ -1853,7 +1853,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Fl_ief.html b/build/emd_Fl_ief.html
index a17e094..1444ee2 100644
--- a/build/emd_Fl_ief.html
+++ b/build/emd_Fl_ief.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,7 +1637,7 @@ law in integral form:
 
 
 
-<div class="example div" id="orgfcd2e61">
+<div class="example div" id="org2badd21">
 <p>
 <b>Example: loop with time-dependent flux</b>
 </p>
@@ -1664,7 +1664,7 @@ Increasing \({\bf B}\):  clockwise (viewed from above) \({\bf E}\) from Lenz.
 </div>
 
 
-<div class="example div" id="orgafdd47c">
+<div class="example div" id="org6994570">
 <p>
 <b>Example: wheel with charged rim traversed by flux</b>
 </p>
@@ -1705,7 +1705,7 @@ called the <b>quasistatic</b> approximation, and works provided we deal with
 <i>slow enough</i> phenomena.
 </p>
 
-<div class="example div" id="org6631fcc">
+<div class="example div" id="orgddce4f1">
 <p>
 <b>Example: field from wire with time-dependent current</b>
 </p>
@@ -1764,7 +1764,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Me.html b/build/emd_Me.html
index 6580b87..824752b 100644
--- a/build/emd_Me.html
+++ b/build/emd_Me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Me_Me.html b/build/emd_Me_Me.html
index 1944a1a..047e313 100644
--- a/build/emd_Me_Me.html
+++ b/build/emd_Me_Me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,18 +1616,18 @@ Table of contents
 <p>
 Full set of equations for the electromagnetic field:
 </p>
-<div class="core div" id="org71429ce">
+<div class="core div" id="org96eda60">
 <p>
 <b>Maxwell's equations</b> <i>(in vacuum)</i>
 </p>
-<div class="eqlabel" id="org92aa36d">
+<div class="eqlabel" id="org99bc512">
 <p>
 <a id="Max_vac"></a><a href="./emd_Me_Me.html#Max_vac"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd8ea0a7">
+<div class="alteqlabels" id="org0385504">
 
 </div>
 
@@ -1644,7 +1644,7 @@ Full set of equations for the electromagnetic field:
 <p>
 Complement:
 </p>
-<div class="core div" id="org93d1ad6">
+<div class="core div" id="org8bd62bd">
 <p>
 Force law <a href="./ems_ms_lf_pc.html#LorFo">LorFo</a>
 \[
@@ -1667,15 +1667,15 @@ take divergence of \((iv)\) and use \((i)\).
 <p>
 Better way of writing:  all fields on left, all sources on right,
 </p>
-<div class="core div" id="org82c9083">
-<div class="eqlabel" id="org1583626">
+<div class="core div" id="org3b3efc0">
+<div class="eqlabel" id="orgaa87be2">
 <p>
 <a id="Max_vac_s"></a><a href="./emd_Me_Me.html#Max_vac_s"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgfc0a16c">
+<div class="alteqlabels" id="org3e69b1d">
 <ul class="org-ul">
 <li>Gr (7.42)</li>
 </ul>
@@ -1713,7 +1713,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Me_dc.html b/build/emd_Me_dc.html
index 3b7c053..e4c37f9 100644
--- a/build/emd_Me_dc.html
+++ b/build/emd_Me_dc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1622,15 +1622,15 @@ The term which should be zero (but isn't) in <a href="./emd_Me_ebM.html#divcurlB
 \]
 The extra term would thus be eliminated if we were to put
 </p>
-<div class="core div" id="orgfb244bd">
-<div class="eqlabel" id="org02e358a">
+<div class="core div" id="org65d0a3c">
+<div class="eqlabel" id="org2343c92">
 <p>
 <a id="AmpMax"></a><a href="./emd_Me_dc.html#AmpMax"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf266507">
+<div class="alteqlabels" id="org09fe122">
 <ul class="org-ul">
 <li>Gr (7.36)</li>
 </ul>
@@ -1659,18 +1659,18 @@ Real confirmation of Maxwell's theory:  1888, Hertz's experiments on propagation
 <p>
 Maxwell baptized this term the
 </p>
-<div class="core div" id="orgb3e1688">
+<div class="core div" id="org9a1c650">
 <p>
 <b>Displacement current</b>
 </p>
-<div class="eqlabel" id="org5bc6ac9">
+<div class="eqlabel" id="orgea96ca5">
 <p>
 <a id="Jd"></a><a href="./emd_Me_dc.html#Jd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2273d93">
+<div class="alteqlabels" id="org147727a">
 <ul class="org-ul">
 <li>Gr (7.37)</li>
 </ul>
@@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Me_ebM.html b/build/emd_Me_ebM.html
index b3cbec5..4fa7a93 100644
--- a/build/emd_Me_ebM.html
+++ b/build/emd_Me_ebM.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1630,14 +1630,14 @@ Fatal inconsistency:  div of curl must always vanish.  Check on \((iii)\):
 \]
 But:  try same with \((iv)\):
 </p>
-<div class="eqlabel" id="org1332a90">
+<div class="eqlabel" id="org5adad0c">
 <p>
 <a id="divcurlB"></a><a href="./emd_Me_ebM.html#divcurlB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc919b58">
+<div class="alteqlabels" id="orga04de46">
 <ul class="org-ul">
 <li>Gr (7.35)</li>
 </ul>
@@ -1682,7 +1682,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_Me_mc.html b/build/emd_Me_mc.html
index 08849f6..a64a5ee 100644
--- a/build/emd_Me_mc.html
+++ b/build/emd_Me_mc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1663,7 +1663,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce.html b/build/emd_ce.html
index 3c77cc0..1154b3f 100644
--- a/build/emd_ce.html
+++ b/build/emd_ce.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emd.ce</span></h3>
 
 <div class="outline-text-3" id="text-emd_ce">
-<details class="prereq" id="org4aea2a7">
-<summary id="orgbb42f82">
+<details class="prereq" id="orgbcfd9aa">
+<summary id="orgfd4a1b6">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1623,8 +1623,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="orgacf1d30">
-<summary id="org560d61d">
+<details class="objectives" id="orgb58d097">
+<summary id="org5cd5f85">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1662,7 +1662,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce_amom.html b/build/emd_ce_amom.html
index 16b550a..be0150b 100644
--- a/build/emd_ce_amom.html
+++ b/build/emd_ce_amom.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,18 +1616,18 @@ Table of contents
 <p>
 The angular momentum of EM fields is directly given by
 </p>
-<div class="main div" id="org8982815">
+<div class="main div" id="orgc2d5343">
 <p>
 <b>Angular momentum of EM fields</b>
 </p>
-<div class="eqlabel" id="org8297ce4">
+<div class="eqlabel" id="orgd4d0682">
 <p>
 <a id="lrxg"></a><a href="./emd_ce_amom.html#lrxg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc1dccb2">
+<div class="alteqlabels" id="orgf246c58">
 
 </div>
 
@@ -1661,7 +1661,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce_ce.html b/build/emd_ce_ce.html
index d5ec10d..93cabe8 100644
--- a/build/emd_ce_ce.html
+++ b/build/emd_ce_ce.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,7 +1635,7 @@ This means that
 \]
 Since this is true for any volume, we have (re)derived the
 </p>
-<div class="core div" id="org1d21244">
+<div class="core div" id="orgc746662">
 <p>
 <b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
 \[
@@ -1675,7 +1675,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce_mom.html b/build/emd_ce_mom.html
index 1510ed0..f6ea3d5 100644
--- a/build/emd_ce_mom.html
+++ b/build/emd_ce_mom.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1628,18 +1628,18 @@ in which the first integral can be interpreted as the momentum stored in the EM
 <p>
 This is thus simply a conservation law for momentum, with
 </p>
-<div class="main div" id="orgbd3d67d">
+<div class="main div" id="org9032358">
 <p>
 <b>Momentum density in the EM fields</b>
 </p>
-<div class="eqlabel" id="org2b66251">
+<div class="eqlabel" id="org0649d73">
 <p>
 <a id="gExB"></a><a href="./emd_ce_mom.html#gExB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org006aaa0">
+<div class="alteqlabels" id="org7dc7b00">
 
 </div>
 
@@ -1655,18 +1655,18 @@ This is thus simply a conservation law for momentum, with
 <p>
 In a region in which the mechanical momentum is not changing due to external influences, we then have the
 </p>
-<div class="main div" id="orgd647d42">
+<div class="main div" id="org72dfdb8">
 <p>
 <b>Continuity equation for EM momentum</b>
 </p>
-<div class="eqlabel" id="org84364f8">
+<div class="eqlabel" id="org89a6b5f">
 <p>
 <a id="contg"></a><a href="./emd_ce_mom.html#contg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org03c5d23">
+<div class="alteqlabels" id="orgd3a1580">
 
 </div>
 
@@ -1699,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce_mst.html b/build/emd_ce_mst.html
index 67ffc16..82776a6 100644
--- a/build/emd_ce_mst.html
+++ b/build/emd_ce_mst.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1667,18 +1667,18 @@ and similarly for \({\boldsymbol B}\). We thus get
 <p>
 This expression can be greatly simplified by introducing the
 </p>
-<div class="main div" id="org63be843">
+<div class="main div" id="orge483101">
 <p>
 <b>Maxwell stress tensor</b>
 </p>
-<div class="eqlabel" id="org7c75f9d">
+<div class="eqlabel" id="org42e9f16">
 <p>
 <a id="MaxST"></a><a href="./emd_ce_mst.html#MaxST"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd84a618">
+<div class="alteqlabels" id="orgf3e9098">
 
 </div>
 
@@ -1699,18 +1699,18 @@ The element \(T_{ij}\) represents the force per unit area in the \(i\) direction
 <p>
 We then obtain the
 </p>
-<div class="main div" id="orgfeaab67">
+<div class="main div" id="org3664d29">
 <p>
 <b>EM force per unit volume</b>
 </p>
-<div class="eqlabel" id="org9fc5057">
+<div class="eqlabel" id="org6136353">
 <p>
 <a id="fT"></a><a href="./emd_ce_mst.html#fT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgecbfdae">
+<div class="alteqlabels" id="org7273a9f">
 
 </div>
 
@@ -1726,18 +1726,18 @@ We then obtain the
 <p>
 where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
 </p>
-<div class="main div" id="org86829bd">
+<div class="main div" id="org2a4f340">
 <p>
 <b>Total force on charges in volume</b>
 </p>
-<div class="eqlabel" id="org2370cf3">
+<div class="eqlabel" id="org0298272">
 <p>
 <a id="totFo"></a><a href="./emd_ce_mst.html#totFo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc55376c">
+<div class="alteqlabels" id="org1024eff">
 
 </div>
 
@@ -1770,7 +1770,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_ce_poy.html b/build/emd_ce_poy.html
index 75edee8..9fd22fb 100644
--- a/build/emd_ce_poy.html
+++ b/build/emd_ce_poy.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,14 +1636,14 @@ done by EM forces?  From Lorentz force law:
 Really, we're looking at a small volume element \(d\tau\) carrying charge \(\rho d\tau\), moving
 at velocity \({\bf v}\) such that \({\bf J} = \rho {\bf v}\).  Thus,
 </p>
-<div class="eqlabel" id="orge2567ac">
+<div class="eqlabel" id="org0c693e0">
 <p>
 <a id="dWdt_intEJ"></a><a href="./emd_ce_poy.html#dWdt_intEJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org4d05a80">
+<div class="alteqlabels" id="orge34a4b7">
 <ul class="org-ul">
 <li>Gr (8.6)</li>
 </ul>
@@ -1683,18 +1683,18 @@ so we get
 Substituting this in <a href="./emd_ce_poy.html#dWdt_intEJ">dWdt_intEJ</a> and using the divergence theorem,
 we obtain
 </p>
-<div class="main div" id="org36db96e">
+<div class="main div" id="orgb7d7869">
 <p>
 <b>Poynting's theorem</b>
 </p>
-<div class="eqlabel" id="org21ce6b8">
+<div class="eqlabel" id="org1a4b16b">
 <p>
 <a id="👉Thm"></a><a href="./emd_ce_poy.html#👉Thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org09a112b">
+<div class="alteqlabels" id="org4feadff">
 <ul class="org-ul">
 <li>Gr (8.9)</li>
 </ul>
@@ -1720,18 +1720,18 @@ energy is carried by EM fields out of \({\cal V}\) across its boundary surface.
 <p>
 Energy per unit time, per unit area carried by EM fields: given by the
 </p>
-<div class="core div" id="org0bf3f6c">
+<div class="core div" id="orgdc56ce9">
 <p>
 <b>Poynting vector</b>
 </p>
-<div class="eqlabel" id="org327095e">
+<div class="eqlabel" id="orga61d997">
 <p>
 <a id="PoyntingVec"></a><a href="./emd_ce_poy.html#PoyntingVec"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7684a8e">
+<div class="alteqlabels" id="orgb7a4cb9">
 <ul class="org-ul">
 <li>Gr (8.10)</li>
 </ul>
@@ -1750,18 +1750,18 @@ Energy per unit time, per unit area carried by EM fields: given by the
 <p>
 We can thus express Poynting's theorem more compactly:
 </p>
-<div class="core div" id="org4255191">
+<div class="core div" id="orgd48d57f">
 <p>
 <b>Poynting's theorem</b> (integral form)
 </p>
-<div class="eqlabel" id="orgd0524d3">
+<div class="eqlabel" id="org32c9daf">
 <p>
 <a id="PoyntingThm_int"></a><a href="./emd_ce_poy.html#PoyntingThm_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8acaa16">
+<div class="alteqlabels" id="org59d2761">
 <ul class="org-ul">
 <li>Gr (8.11)</li>
 </ul>
@@ -1780,18 +1780,18 @@ We can thus express Poynting's theorem more compactly:
 <p>
 where we have defined the total
 </p>
-<div class="core div" id="org85e77e2">
+<div class="core div" id="org5e10531">
 <p>
 <b>Energy in electromagnetic fields</b>
 </p>
-<div class="eqlabel" id="org7d4ae3d">
+<div class="eqlabel" id="orgad6f50f">
 <p>
 <a id="Uem"></a><a href="./emd_ce_poy.html#Uem"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7a55647">
+<div class="alteqlabels" id="orga3df7bc">
 <ul class="org-ul">
 <li>Gr (8.5)</li>
 </ul>
@@ -1820,18 +1820,18 @@ Then,
 \]
 so we get the
 </p>
-<div class="core div" id="orgbdb096d">
+<div class="core div" id="orgb7a11e9">
 <p>
 <b>Poynting theorem</b> (differential form)
 </p>
-<div class="eqlabel" id="org9c56948">
+<div class="eqlabel" id="orga2e5c79">
 <p>
 <a id="PoyntingThm"></a><a href="./emd_ce_poy.html#PoyntingThm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdfe3994">
+<div class="alteqlabels" id="org0cf780d">
 <ul class="org-ul">
 <li>Gr (8.14)</li>
 </ul>
@@ -1854,7 +1854,7 @@ and has a similar for to the continuity equation
 
 
 
-<div class="example div" id="org15b725b">
+<div class="example div" id="org1083447">
 <p>
 <b>Example:  Joule heating</b>
 </p>
@@ -1911,7 +1911,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_emw.html b/build/emd_emw.html
index 494963b..a63af3a 100644
--- a/build/emd_emw.html
+++ b/build/emd_emw.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emd.emw</span></h3>
 
 <div class="outline-text-3" id="text-emd_emw">
-<details class="prereq" id="org17a8cef">
-<summary id="org45e360a">
+<details class="prereq" id="org92d8d0c">
+<summary id="orgb97228e">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1624,8 +1624,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="org91615eb">
-<summary id="orgec366bf">
+<details class="objectives" id="org5c24096">
+<summary id="orge645495">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_emw_ep.html b/build/emd_emw_ep.html
index 441d2bb..3ae2cc6 100644
--- a/build/emd_emw_ep.html
+++ b/build/emd_emw_ep.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1644,18 +1644,18 @@ so for a monochromatic EM plan wave,
 \]
 or more succinctly:
 </p>
-<div class="main div" id="orgdf4b8bc">
+<div class="main div" id="orga5c9575">
 <p>
 <b>Poynting vector of a monochromatic EM wave</b>
 </p>
-<div class="eqlabel" id="org3913519">
+<div class="eqlabel" id="org72a5a32">
 <p>
 <a id="Poynting_mpw"></a><a href="./emd_emw_ep.html#Poynting_mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8b59092">
+<div class="alteqlabels" id="org7e5d7a7">
 <ul class="org-ul">
 <li>Gr (9.57)</li>
 </ul>
@@ -1678,7 +1678,7 @@ This has a transparent physical interpretation: the energy density \(u\) flows w
 <p>
 Similary, we get the
 </p>
-<div class="main div" id="org21912bb">
+<div class="main div" id="orgd6eada9">
 <p>
 <b>Momentum density of a monochromatic EM wave</b>
 \[
@@ -1729,7 +1729,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_emw_mpw.html b/build/emd_emw_mpw.html
index 665b048..5f1fa9c 100644
--- a/build/emd_emw_mpw.html
+++ b/build/emd_emw_mpw.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,14 +1636,14 @@ From Faraday:  \({\boldsymbol \nabla} \times {\bf E} = -\partial {\bf B}/\partia
 \]
 so \({\bf E}\) and \({\bf B}\) are mutually perpendicular, and
 </p>
-<div class="eqlabel" id="org619c73f">
+<div class="eqlabel" id="org44bb1e2">
 <p>
 <a id="EBmpw"></a><a href="./emd_emw_mpw.html#EBmpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgaad096d">
+<div class="alteqlabels" id="org0064233">
 <ul class="org-ul">
 <li>Gr (9.47)</li>
 </ul>
@@ -1662,18 +1662,18 @@ B_0 = \frac{k}{\omega} E_0 = \frac{1}{c} E_0.
 Generalizing to propagation in the direction of an arbitrary wavevector
 \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
 </p>
-<div class="core div" id="org9c77e17">
+<div class="core div" id="org83aeece">
 <p>
 <b>E and B fields for a monochromatic EM plane wave</b>
 </p>
-<div class="eqlabel" id="org54506e2">
+<div class="eqlabel" id="org82e71ea">
 <p>
 <a id="mpw"></a><a href="./emd_emw_mpw.html#mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb384c79">
+<div class="alteqlabels" id="orgb1b901e">
 <ul class="org-ul">
 <li>Gr (9.49)</li>
 </ul>
@@ -1724,7 +1724,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emd_emw_we.html b/build/emd_emw_we.html
index f8b6db0..27c61a0 100644
--- a/build/emd_emw_we.html
+++ b/build/emd_emw_we.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1641,18 +1641,18 @@ These take the form of coupled first-order partial differential equations for \(
 Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
 we get the
 </p>
-<div class="core div" id="org0b3ebdc">
+<div class="core div" id="orge19d256">
 <p>
 <b>Wave equations for electric and magnetic fields in vacuum</b>
 </p>
-<div class="eqlabel" id="orge465a34">
+<div class="eqlabel" id="orgff19c15">
 <p>
 <a id="WaveEq"></a><a href="./emd_emw_we.html#WaveEq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org3ff5ea0">
+<div class="alteqlabels" id="orga8c7165">
 <ul class="org-ul">
 <li>Gr (9.41)</li>
 </ul>
@@ -1714,7 +1714,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm.html b/build/emdm.html
index 770533d..099e2ad 100644
--- a/build/emdm.html
+++ b/build/emdm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_Me.html b/build/emdm_Me.html
index 95191e9..672c7a2 100644
--- a/build/emdm_Me.html
+++ b/build/emdm_Me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_Me_Mem.html b/build/emdm_Me_Mem.html
index f1e2b53..1263e23 100644
--- a/build/emdm_Me_Mem.html
+++ b/build/emdm_Me_Mem.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1648,18 +1648,18 @@ dI = \frac{\partial \sigma_b}{\partial t} da_{\perp} = \frac{\partial P}{\partia
 \]
 We therefore have the
 </p>
-<div class="core div" id="org64396a0">
+<div class="core div" id="orgc00904a">
 <p>
 <b>Polarization current density</b>
 </p>
-<div class="eqlabel" id="orgf37fc4f">
+<div class="eqlabel" id="org3742df8">
 <p>
 <a id="Jp"></a><a href="./emdm_Me_Mem.html#Jp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org12af1ad">
+<div class="alteqlabels" id="org6073635">
 <ul class="org-ul">
 <li>Gr (7.48)</li>
 </ul>
@@ -1683,7 +1683,7 @@ the polarization current is the result of linear motion of charge when
 polarization changes).  We can check consistency with the continuity equation
 associated to the conservation of bound charges:
 </p>
-<aside id="org0322793">
+<aside id="orgff2c75f">
 <p>
 Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current \({\boldsymbol J}_b\) but this is not the common convention.
 </p>
@@ -1705,15 +1705,15 @@ Changing magnetization does not lead to analogous accumulation of charge and cur
 In view of this:  total charge density can be separated into 2 parts,
 <b>free</b> and <b>bound</b>:
 </p>
-<div class="main div" id="org56027a6">
-<div class="eqlabel" id="org6fd2aed">
+<div class="main div" id="org7866a36">
+<div class="eqlabel" id="orge94a27e">
 <p>
 <a id="rhofb"></a><a href="./emdm_Me_Mem.html#rhofb"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org9e03f13">
+<div class="alteqlabels" id="orgbb91da6">
 <ul class="org-ul">
 <li>Gr (7.49)</li>
 </ul>
@@ -1733,15 +1733,15 @@ In view of this:  total charge density can be separated into 2 parts,
 and current can be separated into three parts, <b>free</b>, <b>bound</b> and
 <b>polarization</b>:
 </p>
-<div class="main div" id="org96443a3">
-<div class="eqlabel" id="orga6b8e4a">
+<div class="main div" id="org765eeee">
+<div class="eqlabel" id="org49803b2">
 <p>
 <a id="Jfbp"></a><a href="./emdm_Me_Mem.html#Jfbp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgddcfaf9">
+<div class="alteqlabels" id="orgc87ffc7">
 <ul class="org-ul">
 <li>Gr (7.50)</li>
 </ul>
@@ -1767,7 +1767,7 @@ Gauss's law:  can be rewritten
 \]
 where (as in static case)
 </p>
-<div class="core div" id="orgdbd92f1">
+<div class="core div" id="org91a1e38">
 <p>
 \[
 {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
@@ -1788,7 +1788,7 @@ or
 \]
 where as before
 </p>
-<div class="core div" id="org7839f4c">
+<div class="core div" id="org0c2e84f">
 <p>
 \[
 {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
@@ -1806,18 +1806,18 @@ bound parts, since they don't involve \(\rho\) or \({\bf J}\).
 <p>
 In terms of free charges and currents, we thus get
 </p>
-<div class="core div" id="org6597738">
+<div class="core div" id="orgeeb0b35">
 <p>
 <b>Maxwell's equations</b> <i>(in matter)</i>
 </p>
-<div class="eqlabel" id="orgffcbbe9">
+<div class="eqlabel" id="orgb9e6675">
 <p>
 <a id="Max_mat"></a><a href="./emdm_Me_Mem.html#Max_mat"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5c6c62d">
+<div class="alteqlabels" id="org6367cef">
 <ul class="org-ul">
 <li>Gr (7.55)</li>
 </ul>
@@ -1847,15 +1847,15 @@ This must all be complemented by the <b>constitutive relations</b> giving \({\bf
 in terms of \({\bf E}\) and \({\bf B}\).
 For the restricted case of linear media:
 </p>
-<div class="main div" id="org2d4f8dd">
-<div class="eqlabel" id="org03c06a4">
+<div class="main div" id="orgd78e0b5">
+<div class="eqlabel" id="org86e1a29">
 <p>
 <a id="consrel"></a><a href="./emdm_Me_Mem.html#consrel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org45b4fff">
+<div class="alteqlabels" id="org7ea2c8c">
 <ul class="org-ul">
 <li>Gr (7.56,7.57)</li>
 </ul>
@@ -1898,7 +1898,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_Me_bc.html b/build/emdm_Me_bc.html
index 048eac2..b8ced46 100644
--- a/build/emdm_Me_bc.html
+++ b/build/emdm_Me_bc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,18 +1616,18 @@ Table of contents
 <p>
 Discontinuities between different media, deduced from
 </p>
-<div class="core div" id="orgb7aedd2">
+<div class="core div" id="org876a60b">
 <p>
 <b>Maxwell's equations</b> <i>(in matter)</i>, <i>integral form</i>
 </p>
-<div class="eqlabel" id="org6c267cc">
+<div class="eqlabel" id="orga776629">
 <p>
 <a id="Max_mat_int"></a><a href="./emdm_Me_bc.html#Max_mat_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8952960">
+<div class="alteqlabels" id="org6c05186">
 
 </div>
 
@@ -1645,15 +1645,15 @@ Discontinuities between different media, deduced from
 Applying \((i)\) to wafer-thin Gaussian pillbox straddling boundary between 2 materials:
 \({\bf D}_1 \cdot {\bf a} - {\bf D}_2 \cdot {\bf a} = \sigma_f a\) so
 </p>
-<div class="main div" id="orgf92353e">
-<div class="eqlabel" id="orgb9a9a3d">
+<div class="main div" id="org8d20540">
+<div class="eqlabel" id="org7926d65">
 <p>
 <a id="Ddisc"></a><a href="./emdm_Me_bc.html#Ddisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga6c409d">
+<div class="alteqlabels" id="orge1fcf9c">
 <ul class="org-ul">
 <li>Gr (7.60)</li>
 </ul>
@@ -1672,9 +1672,9 @@ D^{\perp}_1 - D^{\perp}_2 = \sigma_f
 <p>
 Same reasoning applied to \((ii)\) gives <a href="./ems_ms_vp_mbc.html#Bdisc">Bdisc</a>
 </p>
-<div class="main div" id="orga22be6d">
-<div class="eqlabel" id="orge0d8321">
-<div class="alteqlabels" id="orgb94a831">
+<div class="main div" id="orgfa3145b">
+<div class="eqlabel" id="orgddc00f3">
+<div class="alteqlabels" id="org80b4003">
 
 </div>
 
@@ -1690,7 +1690,7 @@ B^{\perp}_1 - B^{\perp}_2 = 0
 For \((iii)\):  Amperian loop straddling surface:  \({\bf E}_1 \cdot {\bf l} - {\bf E}_2 \cdot {\bf l} =
 -\frac{d}{dt} \int_{\cal S} {\bf B} \cdot d{\bf a}\).  Limit of small loop:  flux vanishes, therefore
 </p>
-<div class="main div" id="org55a1d42">
+<div class="main div" id="org2dd2bbb">
 <p>
 \[
 {\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0
@@ -1704,7 +1704,7 @@ No volume current can contribute, but a surface current can.  Can write
 \(I_{f_{enc}} = {\bf K}_f \cdot (\hat{\bf n} \times {\bf l}) = ({\bf K}_f \times \hat{\bf n}) \cdot {\bf l}\)
 and thus (as we got before in <a href="./emsm_msm_H_A.html#Hdisc">Hdisc</a>)
 </p>
-<div class="main div" id="org4a2ee70">
+<div class="main div" id="orgd223e2f">
 <p>
 \[
 {\bf H}_1^{\parallel} - {\bf H}_2^{\parallel} = {\bf K}_f \times \hat{\bf n}
@@ -1720,15 +1720,15 @@ These are the general boundary conditions for electrodynamics.
 <p>
 In case of linear media:  can be expressed in terms of \({\bf E}\) and \({\bf B}\) alone:
 </p>
-<div class="main div" id="org9e90e47">
-<div class="eqlabel" id="org8bbc727">
+<div class="main div" id="orgaafde6e">
+<div class="eqlabel" id="orge514e83">
 <p>
 <a id="disc_lm"></a><a href="./emdm_Me_bc.html#disc_lm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga51b616">
+<div class="alteqlabels" id="org786e6ec">
 <ul class="org-ul">
 <li>Gr (7.64)</li>
 </ul>
@@ -1748,14 +1748,14 @@ In case of linear media:  can be expressed in terms of \({\bf E}\) and \({\bf B}
 <p>
 If there is no free charge and no free current at boundary:
 </p>
-<div class="eqlabel" id="orgf07dc3e">
+<div class="eqlabel" id="orga74521d">
 <p>
 <a id="disc_nfc"></a><a href="./emdm_Me_bc.html#disc_nfc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdd74046">
+<div class="alteqlabels" id="orgac68624">
 <ul class="org-ul">
 <li>Gr (7.64)</li>
 </ul>
@@ -1792,7 +1792,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm.html b/build/emdm_emwm.html
index a22cf60..d003c91 100644
--- a/build/emdm_emwm.html
+++ b/build/emdm_emwm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emdm.emwm</span></h3>
 
 <div class="outline-text-3" id="text-emdm_emwm">
-<details class="prereq" id="org5c9f997">
-<summary id="orgcac0ec5">
+<details class="prereq" id="org499ec58">
+<summary id="org504cdbb">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1625,8 +1625,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="orgde042c7">
-<summary id="org6ca3c40">
+<details class="objectives" id="org76e4576">
+<summary id="org77d80f7">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1666,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_ad.html b/build/emdm_emwm_ad.html
index 64f1afc..0b9b7c1 100644
--- a/build/emdm_emwm_ad.html
+++ b/build/emdm_emwm_ad.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_ad_c.html b/build/emdm_emwm_ad_c.html
index 85dd41a..3339f8c 100644
--- a/build/emdm_emwm_ad_c.html
+++ b/build/emdm_emwm_ad_c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1733,7 +1733,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_plm.html b/build/emdm_emwm_plm.html
index 56e9cb1..1227e0e 100644
--- a/build/emdm_emwm_plm.html
+++ b/build/emdm_emwm_plm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1632,15 +1632,15 @@ For linear medium:
 \]
 If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
 </p>
-<div class="main div" id="org3abedbf">
-<div class="eqlabel" id="org6c3c992">
+<div class="main div" id="orgead2b1c">
+<div class="eqlabel" id="org9916855">
 <p>
 <a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org4747e62">
+<div class="alteqlabels" id="org5111273">
 <ul class="org-ul">
 <li>Gr (9.65)</li>
 </ul>
@@ -1669,18 +1669,18 @@ v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{n}
 \]
 where the index of refraction of the material is defined as
 </p>
-<div class="main div" id="org92a77a7">
+<div class="main div" id="org5237a1a">
 <p>
 <b>Index of refraction</b>
 </p>
-<div class="eqlabel" id="orgb3ac891">
+<div class="eqlabel" id="org6cb7362">
 <p>
 <a id="n"></a><a href="./emdm_emwm_plm.html#n"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orge10b1d5">
+<div class="alteqlabels" id="orgc12f464">
 <ul class="org-ul">
 <li>Gr (9.69)</li>
 </ul>
@@ -1743,7 +1743,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_refl.html b/build/emdm_emwm_refl.html
index 14efd24..a8891fe 100644
--- a/build/emdm_emwm_refl.html
+++ b/build/emdm_emwm_refl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1649,7 +1649,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_refl_ni.html b/build/emdm_emwm_refl_ni.html
index 2675754..69125bd 100644
--- a/build/emdm_emwm_refl_ni.html
+++ b/build/emdm_emwm_refl_ni.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1671,14 +1671,14 @@ E_{0_I} - E_{0_R} = \beta E_{0_T}, \hspace{1cm}
 Solving these coupled equations, we can write
 outgoing amplitudes in terms of incident ones:
 </p>
-<div class="eqlabel" id="org0451818">
+<div class="eqlabel" id="orgf6ae25d">
 <p>
 <a id="ERT"></a><a href="./emdm_emwm_refl_ni.html#ERT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgca80cb9">
+<div class="alteqlabels" id="org17eb76a">
 <ul class="org-ul">
 <li>Gr (9.82)</li>
 </ul>
@@ -1744,7 +1744,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_refl_oi.html b/build/emdm_emwm_refl_oi.html
index 97ed148..83c63f0 100644
--- a/build/emdm_emwm_refl_oi.html
+++ b/build/emdm_emwm_refl_oi.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,14 +1635,14 @@ Transmitted wave:
 \]
 All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
 </p>
-<div class="eqlabel" id="orgd898837">
+<div class="eqlabel" id="org512368e">
 <p>
 <a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgabe9175">
+<div class="alteqlabels" id="org1361b67">
 
 </div>
 
@@ -1665,7 +1665,7 @@ These forms for incident, reflected and transmitted wave can be substituted in t
 <p>
 From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
 </p>
-<div class="core div" id="org4e7e42a">
+<div class="core div" id="org86dbe79">
 <p>
 <b>First law of reflection:</b>
   the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
@@ -1680,7 +1680,7 @@ Specializing <a href="./emdm_emwm_refl_oi.html#RTobliquek">RTobliquek</a> to our
 with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
 and the angle of refraction (\(\theta_T\)) obey the following laws:
 </p>
-<div class="core div" id="org99d6843">
+<div class="core div" id="orge55fc76">
 <p>
 <b>Law of reflection</b>
   \[
@@ -1697,14 +1697,14 @@ and the angle of refraction (\(\theta_T\)) obey the following laws:
 <p>
 This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
 </p>
-<div class="eqlabel" id="orgdc0e7b2">
+<div class="eqlabel" id="orga2e8f02">
 <p>
 <a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6d39cd4">
+<div class="alteqlabels" id="org12decff">
 
 </div>
 
@@ -1750,18 +1750,18 @@ while the third equation becomes
 \]
 Writing everything in terms of the incident amplitude, we get
 </p>
-<div class="main div" id="org1929cd0">
+<div class="main div" id="org29006a2">
 <p>
 <b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
 </p>
-<div class="eqlabel" id="org0b8be69">
+<div class="eqlabel" id="orgd431e6b">
 <p>
 <a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org617a8e4">
+<div class="alteqlabels" id="orgd3db507">
 
 </div>
 
@@ -1785,15 +1785,15 @@ Amplitudes for transmitted and reflected wave: depend on angle of incidence:
 Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
 For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
 </p>
-<div class="main div" id="org087c316">
-<div class="eqlabel" id="orgb61a423">
+<div class="main div" id="orgff8c46e">
+<div class="eqlabel" id="org7aac922">
 <p>
 <a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org4e4ad5e">
+<div class="alteqlabels" id="orgb13b73c">
 
 </div>
 
@@ -1846,7 +1846,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_refr.html b/build/emdm_emwm_refr.html
index cc40ee4..8b6e15a 100644
--- a/build/emdm_emwm_refr.html
+++ b/build/emdm_emwm_refr.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1633,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_wg.html b/build/emdm_emwm_wg.html
index 53ea6a8..c720c7f 100644
--- a/build/emdm_emwm_wg.html
+++ b/build/emdm_emwm_wg.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_wg_c.html b/build/emdm_emwm_wg_c.html
index 4248574..0d6e4e1 100644
--- a/build/emdm_emwm_wg_c.html
+++ b/build/emdm_emwm_wg_c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1659,7 +1659,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_wg_gw.html b/build/emdm_emwm_wg_gw.html
index 24bf043..fe8ef0e 100644
--- a/build/emdm_emwm_wg_gw.html
+++ b/build/emdm_emwm_wg_gw.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1683,7 +1683,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emdm_emwm_wg_r.html b/build/emdm_emwm_wg_r.html
index 056ce29..7827f30 100644
--- a/build/emdm_emwm_wg_r.html
+++ b/build/emdm_emwm_wg_r.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emf.html b/build/emf.html
index de417fd..0c39537 100644
--- a/build/emf.html
+++ b/build/emf.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emf</span></h2>
 
 <div class="outline-text-2" id="text-emf">
-<details class="prereq" id="org85fb173">
-<summary id="orgdb11421">
+<details class="prereq" id="orgb4e149b">
+<summary id="org0aed1f7">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1623,8 +1623,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="orga59b9df">
-<summary id="orgf26745f">
+<details class="objectives" id="org55d6b09">
+<summary id="org287324e">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1660,7 +1660,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emf_g.html b/build/emf_g.html
index db433bb..6ad3c07 100644
--- a/build/emf_g.html
+++ b/build/emf_g.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1657,7 +1657,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emf_g_Cg.html b/build/emf_g_Cg.html
index fb98451..9a44e30 100644
--- a/build/emf_g_Cg.html
+++ b/build/emf_g_Cg.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1656,7 +1656,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emf_g_Lg.html b/build/emf_g_Lg.html
index 2f14faf..2571102 100644
--- a/build/emf_g_Lg.html
+++ b/build/emf_g_Lg.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,14 +1616,14 @@ Table of contents
 <p>
 A more aesthetic choice is the <b>Lorenz gauge</b>:
 </p>
-<div class="eqlabel" id="orgb29b121">
+<div class="eqlabel" id="org3de3f9b">
 <p>
 <a id="LorenzG"></a><a href="./emf_g_Lg.html#LorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2006eb5">
+<div class="alteqlabels" id="orgc9fe8ca">
 
 </div>
 
@@ -1635,14 +1635,14 @@ A more aesthetic choice is the <b>Lorenz gauge</b>:
 \]
 which is chosen to put the second term in the left-hand side of <a href="./emf_svp.html#LapA">LapA</a> to zero. What remains is then
 </p>
-<div class="eqlabel" id="orgcba4a5d">
+<div class="eqlabel" id="org5b3094e">
 <p>
 <a id="ALorenzG"></a><a href="./emf_g_Lg.html#ALorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2d4cecb">
+<div class="alteqlabels" id="org687131e">
 
 </div>
 
@@ -1654,14 +1654,14 @@ which is chosen to put the second term in the left-hand side of <a href="./emf_s
 \]
 while the equation for \(\phi\) becomes
 </p>
-<div class="eqlabel" id="org7c6aebc">
+<div class="eqlabel" id="org29d69e0">
 <p>
 <a id="phiLorenzG"></a><a href="./emf_g_Lg.html#phiLorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8b3cda4">
+<div class="alteqlabels" id="org4856773">
 
 </div>
 
@@ -1673,18 +1673,18 @@ while the equation for \(\phi\) becomes
 \]
 These can be written compactly upon introducing a new operator: the
 </p>
-<div class="core div" id="orgd056ba8">
+<div class="core div" id="orga269826">
 <p>
 <b>d'Alembertian operator</b>
 </p>
-<div class="eqlabel" id="orgfd937d0">
+<div class="eqlabel" id="org39fa795">
 <p>
 <a id="dAl"></a><a href="./emf_g_Lg.html#dAl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org57101d6">
+<div class="alteqlabels" id="orgf4aa848">
 
 </div>
 
@@ -1700,18 +1700,18 @@ These can be written compactly upon introducing a new operator: the
 <p>
 so we get the
 </p>
-<div class="core div" id="org037b830">
+<div class="core div" id="org65e01f8">
 <p>
 <b>Inhomogeneous Maxwell equations</b> <i>(Lorenz gauge)</i>
 </p>
-<div class="eqlabel" id="org9dce32f">
+<div class="eqlabel" id="orgc262f70">
 <p>
 <a id="MaxLor"></a><a href="./emf_g_Lg.html#MaxLor"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org22f6c85">
+<div class="alteqlabels" id="orgc540066">
 
 </div>
 
@@ -1764,7 +1764,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emf_svp.html b/build/emf_svp.html
index 30770aa..d5614da 100644
--- a/build/emf_svp.html
+++ b/build/emf_svp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1631,7 +1631,7 @@ Useful strategy: represent fields in terms of potentials.
 Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
 field as a pure curl (since its divergence always vanishes):
 </p>
-<div class="core div" id="org0868f0a">
+<div class="core div" id="org913ae4e">
 <p>
 \[
 {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
@@ -1648,15 +1648,15 @@ Putting this into Faraday's law <a href="./emd_Fl_Fl.html#Fl">Fl</a> gives
 so this can be written as the gradient of a scalar.
 Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
 </p>
-<div class="core div" id="org5ea4990">
-<div class="eqlabel" id="orgccc2c0e">
+<div class="core div" id="orgcc3047e">
+<div class="eqlabel" id="org50da26e">
 <p>
 <a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc2e0dbe">
+<div class="alteqlabels" id="org3a04a5a">
 
 </div>
 
@@ -1673,15 +1673,15 @@ Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
 <p>
 Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
 </p>
-<div class="main div" id="org7ca77db">
-<div class="eqlabel" id="org49309f0">
+<div class="main div" id="orge407b00">
+<div class="eqlabel" id="orgad33676">
 <p>
 <a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1b03eff">
+<div class="alteqlabels" id="org4f2824a">
 
 </div>
 
@@ -1701,15 +1701,15 @@ whereas Ampère-Maxwell becomes
 \]
 which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
 </p>
-<div class="main div" id="org930bf11">
-<div class="eqlabel" id="org7818374">
+<div class="main div" id="orga4d93c1">
+<div class="eqlabel" id="orgbbedeec">
 <p>
 <a id="LapA"></a><a href="./emf_svp.html#LapA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org9e9918d">
+<div class="alteqlabels" id="orgb9a7aee">
 
 </div>
 
@@ -1744,7 +1744,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems.html b/build/ems.html
index 24ab814..5af977f 100644
--- a/build/ems.html
+++ b/build/ems.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca.html b/build/ems_ca.html
index aad9162..9d73e5c 100644
--- a/build/ems_ca.html
+++ b/build/ems_ca.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1618,8 +1618,8 @@ Table of contents
 <li>Gr 3</li>
 </ul>
 
-<details class="prereq" id="orgd0e4e8d">
-<summary id="org949c0df">
+<details class="prereq" id="org587aea3">
+<summary id="orgf03fd4d">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1627,8 +1627,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="orgfb8d074">
-<summary id="org39be3a5">
+<details class="objectives" id="orgedf1d47">
+<summary id="orgbfc64ab">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1666,7 +1666,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_fe.html b/build/ems_ca_fe.html
index b6c14d5..d11df46 100644
--- a/build/ems_ca_fe.html
+++ b/build/ems_ca_fe.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1624,7 +1624,7 @@ A generic configuration of static charges coupled via the Coulomb interaction
 defines an electrostatic problem, whose solution is in principle obtained
 from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
 </p>
-<div class="main div" id="org8236a16">
+<div class="main div" id="orgce1c4bf">
 <p>
 
 </p>
@@ -1638,7 +1638,7 @@ from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_v
 or (often simpler) by calculating the electrostatic potential, using either the
 explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
 </p>
-<div class="main div" id="orgd333b49">
+<div class="main div" id="orge8cb758">
 <p>
 
 </p>
@@ -1658,7 +1658,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
 <a href="./ems_es_ep_PL.html#Poi">🐟</a>
 </p>
 
-<div class="core div" id="orge399a4f">
+<div class="core div" id="org65cda5b">
 <p>
 
 </p>
@@ -1674,7 +1674,7 @@ condition <a href="./ems_es_ef_cE.html#curlE0">curlE0</a> can be expressed as th
 <p>
 In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
 </p>
-<div class="core div" id="orgea54c28">
+<div class="core div" id="org9318a15">
 <p>
 
 </p>
@@ -1712,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_fe_L.html b/build/ems_ca_fe_L.html
index 1ad2b11..8aeeb50 100644
--- a/build/ems_ca_fe_L.html
+++ b/build/ems_ca_fe_L.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1630,14 +1630,14 @@ In one dimension, the potential is a single-variable
 function \(\phi (x)\) and the Laplace equation reads
 </p>
 
-<div class="eqlabel" id="orgd14f5e0">
+<div class="eqlabel" id="orgd38ad90">
 <p>
 <a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdd168eb">
+<div class="alteqlabels" id="org23686dc">
 
 </div>
 
@@ -1652,14 +1652,14 @@ function \(\phi (x)\) and the Laplace equation reads
 <p>
 The solution to this is
 </p>
-<div class="eqlabel" id="org9e3195b">
+<div class="eqlabel" id="org78665cb">
 <p>
 <a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7a39d73">
+<div class="alteqlabels" id="orge0dbdb5">
 <ul class="org-ul">
 <li>Gr (3.6)</li>
 </ul>
@@ -1718,14 +1718,14 @@ In two dimensions, the potential becomes a function
 of two variables (here: \(x\) and \(y\)), so Laplace's
 equation now reads
 </p>
-<div class="eqlabel" id="org01996f8">
+<div class="eqlabel" id="orgd4e7f28">
 <p>
 <a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org518eefc">
+<div class="alteqlabels" id="orga64f9ad">
 
 </div>
 
@@ -1778,14 +1778,14 @@ a point equals its value averaged over a sphere
 \(S_R({\bf r})\) of any radius \(R\) centered on this point
 (and of course not containing any charges),
 </p>
-<div class="eqlabel" id="org1ec3447">
+<div class="eqlabel" id="org598b2e6">
 <p>
 <a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org832c6a2">
+<div class="alteqlabels" id="orgdb48832">
 
 </div>
 
@@ -1797,8 +1797,8 @@ a point equals its value averaged over a sphere
 \]
 </p>
 
-<details id="org653c3ca">
-<summary id="org9063816">
+<details id="orgd997cbe">
+<summary id="org6b22e3f">
 <strong>Physicist's proof</strong>
 </summary>
 <p>
@@ -1860,8 +1860,8 @@ proving the theorem.
 </p>
 </details>
 
-<details id="org086b4a6">
-<summary id="orgd2d3c6e">
+<details id="org2ff5eec">
+<summary id="orgc0446a1">
 <strong>Formal proof</strong>
 </summary>
 
@@ -1911,14 +1911,14 @@ we get the following general
 <p>
 <b>Theorem</b>:
 </p>
-<div class="eqlabel" id="org6d0244a">
+<div class="eqlabel" id="orge37257a">
 <p>
 <a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org227c883">
+<div class="alteqlabels" id="orgb3a7f07">
 
 </div>
 
@@ -1971,19 +1971,19 @@ are necessarily positive, we thus require \(f_x &gt; 0\), \(f_y &gt; 0\) and \(f
 of the \(f_x + f_y + f_z = 0\) condition above.
 </p>
 
-<div class="eqlabel" id="orga00aa93">
+<div class="eqlabel" id="org39eb572">
 <p>
 <a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orge0f050e">
+<div class="alteqlabels" id="org2cc4d11">
 
 </div>
 
 </div>
-<div class="info div" id="org81fcf04">
+<div class="info div" id="orgcd59178">
 <p>
 <b>Earnshaw's theorem (physical version)</b> <br>
 </p>
@@ -2102,7 +2102,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_fe_g.html b/build/ems_ca_fe_g.html
index d8e622c..6a0f0af 100644
--- a/build/ems_ca_fe_g.html
+++ b/build/ems_ca_fe_g.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1613,11 +1613,11 @@ Table of contents
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
 <div class="outline-text-5" id="text-ems_ca_fe_g">
-<div class="info div" id="orgef35f51">
+<div class="info div" id="org60c1b11">
 <p>
 <b>George Green</b>
 </p>
-<aside id="org432d494">
+<aside id="org0b1da41">
 <p>
 See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
 </p>
@@ -1650,14 +1650,14 @@ and
 \]
 Substituting this in the divergence theorem gives <b>Green's first identity</b>
 </p>
-<div class="eqlabel" id="orgfd30f5d">
+<div class="eqlabel" id="org3d01833">
 <p>
 <a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org3125160">
+<div class="alteqlabels" id="orga726fcd">
 <ul class="org-ul">
 <li>J (1.34)</li>
 </ul>
@@ -1675,14 +1675,14 @@ As an aside for now, for completeness, if we do the same thing again but with \(
 interchanged, and subtract the result, we obtain another useful result known as
 <b>Green's second identity</b> or <b>Green's theorem</b>
 </p>
-<div class="eqlabel" id="org028fffd">
+<div class="eqlabel" id="org964d072">
 <p>
 <a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org9ea869b">
+<div class="alteqlabels" id="orge29c408">
 <ul class="org-ul">
 <li>J (1.35)</li>
 </ul>
@@ -1718,7 +1718,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_fe_uP.html b/build/ems_ca_fe_uP.html
index 65304e2..126b9b3 100644
--- a/build/ems_ca_fe_uP.html
+++ b/build/ems_ca_fe_uP.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,14 +1635,14 @@ This yields
 The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
 The right-hand side can be made to vanish if \(\Phi\) obeys either
 </p>
-<div class="eqlabel" id="orgfa460b1">
+<div class="eqlabel" id="org0acb722">
 <p>
 <a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org14f7efc">
+<div class="alteqlabels" id="org03f8c83">
 
 </div>
 
@@ -1654,14 +1654,14 @@ The right-hand side can be made to vanish if \(\Phi\) obeys either
 <p>
 or
 </p>
-<div class="eqlabel" id="orgcd08c73">
+<div class="eqlabel" id="org3d1a359">
 <p>
 <a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6976f14">
+<div class="alteqlabels" id="orga2c0bab">
 
 </div>
 
@@ -1689,19 +1689,19 @@ additive constant.
 <p>
 We can thus finally state the
 </p>
-<div class="eqlabel" id="orgd45117f">
+<div class="eqlabel" id="orgf4dd440">
 <p>
 <a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2d283cb">
+<div class="alteqlabels" id="org786cfb7">
 
 </div>
 
 </div>
-<div class="core div" id="orgf2a5ea9">
+<div class="core div" id="org9b96393">
 <p>
 <b>Uniqueness Theorem</b>
 </p>
@@ -1740,7 +1740,7 @@ Reading other books, you might be misled into thinking that there are numerous c
 and corollaries and that things are
 </p>
 
-<div class="info div" id="orgd298dad">
+<div class="info div" id="org333667e">
 <p>
 <b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
   Do not be misled: there is a <i>unique</i> uniqueness theorem for the
@@ -1767,7 +1767,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me.html b/build/ems_ca_me.html
index afe4669..c81cf2f 100644
--- a/build/ems_ca_me.html
+++ b/build/ems_ca_me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me_Ed.html b/build/ems_ca_me_Ed.html
index afef1aa..57e761c 100644
--- a/build/ems_ca_me_Ed.html
+++ b/build/ems_ca_me_Ed.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1634,14 +1634,14 @@ E_\phi &amp;= -\frac{1}{r \sin \theta} \frac{\partial \phi}{\partial \varphi} =
 <p>
 we get
 </p>
-<div class="eqlabel" id="orgb63ca95">
+<div class="eqlabel" id="org64bd74f">
 <p>
 <a id="E_di_1"></a><a href="./ems_ca_me_Ed.html#E_di_1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgcc89131">
+<div class="alteqlabels" id="org7a09da2">
 <ul class="org-ul">
 <li>Gr (3.103)</li>
 </ul>
@@ -1663,14 +1663,14 @@ E_d ({\bf r}) = - \frac{1}{4\pi \varepsilon_0} \nabla \frac{{\bf p} \cdot {\bf r
 \]
 immediately yielding the coordinate-free expression
 </p>
-<div class="eqlabel" id="org186e651">
+<div class="eqlabel" id="org0c787b9">
 <p>
 <a id="E_di"></a><a href="./ems_ca_me_Ed.html#E_di"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org06f6a5c">
+<div class="alteqlabels" id="orgbecbf32">
 <ul class="org-ul">
 <li>Gr (3.104)</li>
 </ul>
@@ -1710,7 +1710,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me_Eq.html b/build/ems_ca_me_Eq.html
index 0195130..470d43a 100644
--- a/build/ems_ca_me_Eq.html
+++ b/build/ems_ca_me_Eq.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me_a.html b/build/ems_ca_me_a.html
index 94e5a86..5953d91 100644
--- a/build/ems_ca_me_a.html
+++ b/build/ems_ca_me_a.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1628,14 +1628,14 @@ By Taylor expanding, we get
 Formally, we could do this for any vector \({\bf r}_s\) such that \(|{\bf r}_s| &lt; |{\bf r}|\) by
 Taylor expanding with the \({\boldsymbol \nabla}\) operator,
 </p>
-<div class="eqlabel" id="org7b106bc">
+<div class="eqlabel" id="orgb48be32">
 <p>
 <a id="1or_grad"></a><a href="./ems_ca_me_a.html#1or_grad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf9dea72">
+<div class="alteqlabels" id="orge7c3a2e">
 
 </div>
 
@@ -1653,14 +1653,14 @@ the potential takes the form of the general solution of Laplace's equation <a hr
 Reading the parameters, we get \(A_l = 0\), \(B_l = r_s^l\).  Putting back a generic angle
 (the coefficients remain the same), we thus get
 </p>
-<div class="eqlabel" id="org68023ff">
+<div class="eqlabel" id="orgf3ead78">
 <p>
 <a id="1or_Leg"></a><a href="./ems_ca_me_a.html#1or_Leg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org593b10c">
+<div class="alteqlabels" id="orga8fca88">
 <ul class="org-ul">
 <li>Gr(3.94)</li>
 </ul>
@@ -1682,14 +1682,14 @@ we can expand the potential at a point \({\bf r}\) outside \({\cal V}\) accordin
 (here, we put the origin of our coordinate system closer to all points in \({\cal V}\) than to \({\bf r}\)
 to ensure convergence)
 </p>
-<div class="eqlabel" id="orgaf6dad4">
+<div class="eqlabel" id="orgbced9c3">
 <p>
 <a id="p_Leg"></a><a href="./ems_ca_me_a.html#p_Leg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org0904818">
+<div class="alteqlabels" id="org24bf079">
 <ul class="org-ul">
 <li>Gr (3.95)</li>
 </ul>
@@ -1752,14 +1752,14 @@ For \(r \gg d\), we can expand (immediately dropping terms of order \(d^2/r^2\))
 Putting things together, the leading term in the expansion <a href="./ems_ca_me_a.html#p_Leg">p_Leg</a> for the
 potential of the physical dipole is given by
 </p>
-<div class="eqlabel" id="org0b3de33">
+<div class="eqlabel" id="orgfe4f1c4">
 <p>
 <a id="p_physdi"></a><a href="./ems_ca_me_a.html#p_physdi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1803e09">
+<div class="alteqlabels" id="orgf15f43d">
 <ul class="org-ul">
 <li>Gr (3.90)</li>
 </ul>
@@ -1806,7 +1806,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me_h.html b/build/ems_ca_me_h.html
index 12bfdb6..f76b7a9 100644
--- a/build/ems_ca_me_h.html
+++ b/build/ems_ca_me_h.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1621,19 +1621,19 @@ The next terms in the expansion are obtained similarly: the <b>quadrupole</b> te
 \]
 and can be rewritten as
 </p>
-<div class="eqlabel" id="org9893011">
+<div class="eqlabel" id="org51d4992">
 <p>
 <a id="p_quad"></a><a href="./ems_ca_me_h.html#p_quad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8d2b01e">
+<div class="alteqlabels" id="org810939b">
 
 </div>
 
 </div>
-<div class="main div" id="org3dd96b8">
+<div class="main div" id="org72b3bb3">
 <p>
 \[
 \phi_q ({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{1}{2} \sum_{a,b} \frac{r_a r_b}{r^5} Q_{ab}
@@ -1645,19 +1645,19 @@ and can be rewritten as
 <p>
 in terms of the <b>quadrupole moment</b>
 </p>
-<div class="eqlabel" id="org476da28">
+<div class="eqlabel" id="orgfda7b59">
 <p>
 <a id="quadmom"></a><a href="./ems_ca_me_h.html#quadmom"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org3a377ca">
+<div class="alteqlabels" id="orgef3c526">
 
 </div>
 
 </div>
-<div class="main div" id="orgf571492">
+<div class="main div" id="orgff250a4">
 <p>
 \[
 Q_{ab} = \int_{\cal V} d\tau_s (3 r_{s,a} r_{s,b} - r_s^2 \delta_{a,b}) \rho ({\bf r}_s).
@@ -1676,19 +1676,19 @@ This is a symmetric, traceless rank \(2\) tensor: \(Q_{ab} = Q_{ba}\) and
 <p>
 Our expansion for the potential, with terms up to quadrupole ones, thus looks like
 </p>
-<div class="eqlabel" id="org2f1183a">
+<div class="eqlabel" id="org528a861">
 <p>
 <a id="p_mdq"></a><a href="./ems_ca_me_h.html#p_mdq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgae17c12">
+<div class="alteqlabels" id="org4e6d3ec">
 
 </div>
 
 </div>
-<div class="main div" id="org3db4f46">
+<div class="main div" id="org934568d">
 <p>
 \[
 \phi({\bf r}) = \frac{1}{4\pi \varepsilon_0} \left( \frac{Q}{r} + \sum_a \frac{r_a}{r^3} p_a + \frac{1}{2} \sum_{a,b} \frac{r_a r_b}{r^5} Q_{ab} + ... \right)
@@ -1709,7 +1709,7 @@ the leading nonvanishing multipole moment is independent of the chosen location
 the origin of the coordinate system (see Jackson Prob. 4.4).
 </p>
 
-<div class="info div" id="org6c4c92f">
+<div class="info div" id="org4f925ea">
 <p>
 <b>A consistent nomenclature for the multipole expansion?</b>
 </p>
@@ -1858,7 +1858,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_me_md.html b/build/ems_ca_me_md.html
index 9884374..9c193fb 100644
--- a/build/ems_ca_me_md.html
+++ b/build/ems_ca_me_md.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 The series <a href="./ems_ca_me_a.html#p_Leg">p_Leg</a> is organized in increasing powers of inverse distance.
 The leading term is called the *monopole term, and is
 </p>
-<div class="eqlabel" id="org0adcdb6">
+<div class="eqlabel" id="orga2bb8f0">
 <p>
 <a id="p_mono"></a><a href="./ems_ca_me_md.html#p_mono"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc659d6a">
+<div class="alteqlabels" id="org80cce4b">
 <ul class="org-ul">
 <li>Gr (3.97)</li>
 </ul>
@@ -1632,7 +1632,7 @@ The leading term is called the *monopole term, and is
 </div>
 
 </div>
-<div class="core div" id="org46f41ca">
+<div class="core div" id="org93f1445">
 <p>
 \[
 \phi_m ({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{Q}{r}, \hspace{1cm}
@@ -1653,19 +1653,19 @@ The next term is the <b>dipole</b> term:  by using \(P_1 (x) = x\), we have
 \]
 This can be written
 </p>
-<div class="eqlabel" id="orgfa57fa4">
+<div class="eqlabel" id="org000288f">
 <p>
 <a id="p_di"></a><a href="./ems_ca_me_md.html#p_di"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org486bae0">
+<div class="alteqlabels" id="org6eaa92c">
 
 </div>
 
 </div>
-<div class="core div" id="org1702f06">
+<div class="core div" id="org964cce5">
 <p>
 \[
 \phi_d ({\bf r}) = \frac{1}{4\pi \varepsilon_0} \frac{\hat{\bf r} \cdot {\bf p}}{r^2},
@@ -1715,7 +1715,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_mi.html b/build/ems_ca_mi.html
index 460047c..22fbafb 100644
--- a/build/ems_ca_mi.html
+++ b/build/ems_ca_mi.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1646,14 +1646,14 @@ by distance \(d\). For definiteness, we put a charge \(q\) at coordinate
 <p>
 By superposition, we have that
 </p>
-<div class="eqlabel" id="org86b5563">
+<div class="eqlabel" id="orgf44556a">
 <p>
 <a id="p_di_z"></a><a href="./ems_ca_mi.html#p_di_z"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org66c454d">
+<div class="alteqlabels" id="orgd43b156">
 <ul class="org-ul">
 <li>FLS II (6.8)</li>
 <li>Gr (3.9)</li>
@@ -1711,7 +1711,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_mi_fe.html b/build/ems_ca_mi_fe.html
index 33f75b1..2ea31df 100644
--- a/build/ems_ca_mi_fe.html
+++ b/build/ems_ca_mi_fe.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 The force between the point charge and the plane
 is the same as in the case of two point charges:
 </p>
-<div class="eqlabel" id="orga85414d">
+<div class="eqlabel" id="orga3669ce">
 <p>
 <a id="F_dip_z"></a><a href="./ems_ca_mi_fe.html#F_dip_z"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org46b95a1">
+<div class="alteqlabels" id="org1e6fa64">
 <ul class="org-ul">
 <li>Gr (3.12)</li>
 </ul>
@@ -1677,7 +1677,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_mi_isc.html b/build/ems_ca_mi_isc.html
index 34ceef7..7a1803a 100644
--- a/build/ems_ca_mi_isc.html
+++ b/build/ems_ca_mi_isc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 Use <a href="./ems_es_c_sc.html#scd_cond">scd_cond</a>, with the normal direction now
 being \(\hat{\bf z}\):
 </p>
-<div class="eqlabel" id="org3efc1b8">
+<div class="eqlabel" id="org37f029c">
 <p>
 <a id="scd_dip_z"></a><a href="./ems_ca_mi_isc.html#scd_dip_z"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf89ac22">
+<div class="alteqlabels" id="orgbe522ae">
 <ul class="org-ul">
 <li>Gr (3.10)</li>
 </ul>
@@ -1645,14 +1645,14 @@ The total induced charge can be obtained by simple integration as
 Using planar coordinates,
 \(\sigma(r) = \frac{-qd}{4\pi (r^2 + (d/2)^2)^{3/2}}\), so
 </p>
-<div class="eqlabel" id="orgbab70df">
+<div class="eqlabel" id="orge4fbd03">
 <p>
 <a id="sc_dip_z"></a><a href="./ems_ca_mi_isc.html#sc_dip_z"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf3efaa2">
+<div class="alteqlabels" id="org79162af">
 <ul class="org-ul">
 <li>Gr (3.11)</li>
 </ul>
@@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_mi_o.html b/build/ems_ca_mi_o.html
index e8897a5..6e7c6e8 100644
--- a/build/ems_ca_mi_o.html
+++ b/build/ems_ca_mi_o.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1676,7 +1676,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_sv.html b/build/ems_ca_sv.html
index 3776a6a..9ab14ac 100644
--- a/build/ems_ca_sv.html
+++ b/build/ems_ca_sv.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1656,7 +1656,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_sv_car.html b/build/ems_ca_sv_car.html
index eaf5037..868dd08 100644
--- a/build/ems_ca_sv_car.html
+++ b/build/ems_ca_sv_car.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1613,7 +1613,7 @@ Table of contents
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a><span class="headline-id">ems.ca.sv.car</span></h5>
 <div class="outline-text-5" id="text-ems_ca_sv_car">
-<div class="example div" id="org98b3764">
+<div class="example div" id="org4f7c0e6">
 <p>
 
 </p>
@@ -1659,14 +1659,14 @@ This thus falls back onto a 2d problem.  We need to solve the 2d Laplace equatio
 <p>
 Let us look for solutions in the form
 </p>
-<div class="eqlabel" id="orgc28ff62">
+<div class="eqlabel" id="orgf3cdb2d">
 <p>
 <a id="Lap_sv_car"></a><a href="./ems_ca_sv_car.html#Lap_sv_car"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1acbd09">
+<div class="alteqlabels" id="org5ac02b7">
 <ul class="org-ul">
 <li>Gr (3.23)</li>
 </ul>
@@ -1685,14 +1685,14 @@ individual term in the Laplace equation equals a constant,
 and that these constants add up to zero. We can thus put (the sign choice anticipates
 the solution somewhat)
 </p>
-<div class="eqlabel" id="org8e7ab92">
+<div class="eqlabel" id="orgca3ea46">
 <p>
 <a id="Lap_sv_car_sep"></a><a href="./ems_ca_sv_car.html#Lap_sv_car_sep"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org86925b3">
+<div class="alteqlabels" id="orgf06d4b4">
 <ul class="org-ul">
 <li>Gr (3.26)</li>
 </ul>
@@ -1716,14 +1716,14 @@ Let's look first of all at the solutions of <a href="./ems_ca_sv_car.html#Lap_sv
 Since this is a second-order linear differential equation, there are two linearly
 independent solutions.  The most general solution for \(X\) and \(Y\) can be written
 </p>
-<div class="eqlabel" id="orgd404b3a">
+<div class="eqlabel" id="orge369796">
 <p>
 <a id="Lap_sv_car_solXY"></a><a href="./ems_ca_sv_car.html#Lap_sv_car_solXY"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org30886f9">
+<div class="alteqlabels" id="org6d1469c">
 <ul class="org-ul">
 <li>Gr (3.27)</li>
 </ul>
@@ -1780,14 +1780,14 @@ C_n = \frac{2}{a} \int_0^a dy ~\phi_0(y) \sin(n\pi y/a)
 <p>
 <b>Specific example</b>:  say that \(\phi_0(y) = \phi_0\), <i>i.e.</i> just a constant.  Then,
 </p>
-<div class="eqlabel" id="orgf5c8f3f">
+<div class="eqlabel" id="org050a3b2">
 <p>
 <a id="Cn"></a><a href="./ems_ca_sv_car.html#Cn"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5ad8bf2">
+<div class="alteqlabels" id="orgea3f86c">
 <ul class="org-ul">
 <li>Gr (3.35)</li>
 </ul>
@@ -1841,7 +1841,7 @@ The solution for the specific case \(\phi_0 (y) = \phi_0\) is thus
 </p>
 
 
-<div class="example div" id="org8b40fc1">
+<div class="example div" id="orge4fea76">
 <p>
 <b>Example: rectangular pipe</b>
 </p>
@@ -1898,14 +1898,14 @@ The full solution is then a linear combination of complete set of functions,
 The coefficients must be chosen such that \((iii)\) is fulfilled, \(\phi(b,y) = \phi_0\).
 This simple case of a constant value \(\phi_0\) gives us the same relation as <a href="./ems_ca_sv_car.html#Cn">Cn</a>, so
 </p>
-<div class="eqlabel" id="org4c670ac">
+<div class="eqlabel" id="org4b471b1">
 <p>
 <a id="p_recpipe"></a><a href="./ems_ca_sv_car.html#p_recpipe"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdedd5fd">
+<div class="alteqlabels" id="org0968599">
 <ul class="org-ul">
 <li>Gr (3.42)</li>
 </ul>
@@ -1941,7 +1941,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_sv_cyl.html b/build/ems_ca_sv_cyl.html
index c13bd7b..b49d93d 100644
--- a/build/ems_ca_sv_cyl.html
+++ b/build/ems_ca_sv_cyl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1633,7 +1633,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ca_sv_sph.html b/build/ems_ca_sv_sph.html
index 2f8be20..2fe08ff 100644
--- a/build/ems_ca_sv_sph.html
+++ b/build/ems_ca_sv_sph.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 In spherical coordinates, the Laplace equation takes the following form
 (using <a href="./c_m_cs_sph.html#sph_Lap">sph_Lap</a>):
 </p>
-<div class="eqlabel" id="org960f8d0">
+<div class="eqlabel" id="org9243631">
 <p>
 <a id="Lap_sph"></a><a href="./ems_ca_sv_sph.html#Lap_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1c959d0">
+<div class="alteqlabels" id="orgc108761">
 <ul class="org-ul">
 <li>Gr (3.53)</li>
 <li>W (11-86)</li>
@@ -1633,7 +1633,7 @@ In spherical coordinates, the Laplace equation takes the following form
 </div>
 
 </div>
-<div class="main div" id="org973c5fc">
+<div class="main div" id="org2866001">
 <p>
 
 </p>
@@ -1650,14 +1650,14 @@ In spherical coordinates, the Laplace equation takes the following form
 If you are dealing with a problem having <b>azimuthal symmetry</b>,
 \(\phi\) is independent of \(\varphi\) and the equation simplifies to:
 </p>
-<div class="eqlabel" id="orgb049674">
+<div class="eqlabel" id="org464b3a7">
 <p>
 <a id="Lap_sph_az"></a><a href="./ems_ca_sv_sph.html#Lap_sph_az"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org954a313">
+<div class="alteqlabels" id="org9815bac">
 <ul class="org-ul">
 <li>Gr (3.54)</li>
 <li>W (11-87)</li>
@@ -1755,7 +1755,7 @@ This equation is solved by <b>Legendre polynomials</b> of the variable \(\cos \t
 </p>
 
 
-<div class="info div" id="org2ecd100">
+<div class="info div" id="orge95fc44">
 <p>
 <b>Legendre polynomials</b>
 </p>
@@ -1776,14 +1776,14 @@ and conveniently defined (for trigonometric arguments) to obey the orthogonality
 relationship (the reason for the normalization on the right-hand side will become clear later)
 </p>
 
-<div class="eqlabel" id="org4d778e7">
+<div class="eqlabel" id="orgd196155">
 <p>
 <a id="Leg_orth_trig"></a><a href="./ems_ca_sv_sph.html#Leg_orth_trig"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org27ae25a">
+<div class="alteqlabels" id="org0daadc1">
 
 </div>
 
@@ -1798,14 +1798,14 @@ relationship (the reason for the normalization on the right-hand side will becom
 <p>
 This same relation can be more simply written by using the variable \(x = \cos \theta\),
 </p>
-<div class="eqlabel" id="orgaf08cf2">
+<div class="eqlabel" id="org760fd1b">
 <p>
 <a id="Leg_orth"></a><a href="./ems_ca_sv_sph.html#Leg_orth"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7afced6">
+<div class="alteqlabels" id="org23d0d7f">
 
 </div>
 
@@ -1823,14 +1823,14 @@ To get started, we need to define the "seed" polynomial (carrying label \(l=0\))
 To make life easy, we set \(P_0 (x) = 1\). Higher polynomials are then sought in the
 form of power series in \(x\). This leads to the first few Legendre polynomials being:
 </p>
-<div class="eqlabel" id="org5045860">
+<div class="eqlabel" id="orgdc31429">
 <p>
 <a id="Leg_pols"></a><a href="./ems_ca_sv_sph.html#Leg_pols"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org0da2636">
+<div class="alteqlabels" id="org0f77fac">
 
 </div>
 
@@ -1850,14 +1850,14 @@ P_5 (x) &amp;= \frac{1}{8} (63x^5 - 70x^3 + 15x).
 The prefactor (and thus the factor in the orthogonality relations <a href="./ems_ca_sv_sph.html#Leg_orth_trig">Leg_orth_trig</a> and the equivalent <a href="./ems_ca_sv_sph.html#Leg_orth">Leg_orth</a> is chosen for convenience such that each polynomial
 takes the value \(1\) when evaluated at argument \(x = 1\),
 </p>
-<div class="eqlabel" id="org234cd5e">
+<div class="eqlabel" id="org4dfddbe">
 <p>
 <a id="Pl_1_1"></a><a href="./ems_ca_sv_sph.html#Pl_1_1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd9a5971">
+<div class="alteqlabels" id="org7633d23">
 
 </div>
 
@@ -1873,14 +1873,14 @@ P_l(1) = 1
 <p>
 The Legendre polynomial \(P_l\) obeys the differential equation
 </p>
-<div class="eqlabel" id="org20460a3">
+<div class="eqlabel" id="org2b73241">
 <p>
 <a id="Leg_de_trig"></a><a href="./ems_ca_sv_sph.html#Leg_de_trig"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf97a64a">
+<div class="alteqlabels" id="orgc06b5cd">
 
 </div>
 
@@ -1892,14 +1892,14 @@ The Legendre polynomial \(P_l\) obeys the differential equation
 \]
 or equivalently
 </p>
-<div class="eqlabel" id="org25bc290">
+<div class="eqlabel" id="orged631e3">
 <p>
 <a id="Leg_de"></a><a href="./ems_ca_sv_sph.html#Leg_de"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org3caf6ac">
+<div class="alteqlabels" id="org3cb5fe1">
 
 </div>
 
@@ -1915,14 +1915,14 @@ or equivalently
 A particularly convenient formula for deriving \(P_l(x)\)
 is the <b>Rodrigues formula</b>:
 </p>
-<div class="eqlabel" id="orgb07c11e">
+<div class="eqlabel" id="org55ec248">
 <p>
 <a id="Rodrigues"></a><a href="./ems_ca_sv_sph.html#Rodrigues"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgff8e527">
+<div class="alteqlabels" id="orgdee9d6b">
 
 </div>
 
@@ -1938,14 +1938,14 @@ P_l(x) = \frac{1}{2^l l!} \left( \frac{d}{dx} \right)^l (x^2 - 1)^l
 <p>
 Actually, a more practical formula is <b>Bonnet's recursion relation</b>
 </p>
-<div class="eqlabel" id="org91981a9">
+<div class="eqlabel" id="org1d3acfd">
 <p>
 <a id="Bonnet"></a><a href="./ems_ca_sv_sph.html#Bonnet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1046201">
+<div class="alteqlabels" id="orgd631ecf">
 
 </div>
 
@@ -1981,14 +1981,14 @@ We therefore come to the culmination of our efforts here, and write
 the general solution to <i>any</i> problem with azimuthal symmetry
 (for which the potential takes a finite value for \(\theta = 0, \pi\)) as
 </p>
-<div class="eqlabel" id="org3bd5c2b">
+<div class="eqlabel" id="orgb35f0cb">
 <p>
 <a id="Lap_sph_az_sol"></a><a href="./ems_ca_sv_sph.html#Lap_sph_az_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd15cd63">
+<div class="alteqlabels" id="org8d2700b">
 <ul class="org-ul">
 <li>Gr (3.65)</li>
 </ul>
@@ -1996,7 +1996,7 @@ the general solution to <i>any</i> problem with azimuthal symmetry
 </div>
 
 </div>
-<div class="main div" id="orgfae9cbf">
+<div class="main div" id="org8b57fc8">
 <p>
 \[
 \phi(r,\theta) = \sum_{l=0}^{\infty} \left( A_l r^l + \frac{B_l}{r^{l+1}} \right) P_l (\cos \theta)
@@ -2008,7 +2008,7 @@ the general solution to <i>any</i> problem with azimuthal symmetry
 
 
 
-<div class="example div" id="orgdf8fb7a">
+<div class="example div" id="org03072a7">
 <p>
 <b>Example: potential inside a hollow sphere</b>
 </p>
@@ -2091,7 +2091,7 @@ Thus, \(A_0 = k/2\), \(A_1 = -k/2\), and all others are zero, so
 </div>
 
 
-<div class="example div" id="org7d1e98d">
+<div class="example div" id="orge6863ac">
 <p>
 <b>Example: surface charge density on sphere</b>
 </p>
@@ -2221,14 +2221,14 @@ A_1^i = \frac{k}{2\varepsilon_0} \int_0^\pi d\theta \sin \theta [P_l(\cos \theta
 <p>
 The potential inside/outside the sphere is then
 </p>
-<div class="eqlabel" id="orgf34445a">
+<div class="eqlabel" id="org18097a4">
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 <a id="p_uni_ch_sph"></a><a href="./ems_ca_sv_sph.html#p_uni_ch_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5858176">
+<div class="alteqlabels" id="orgce76611">
 
 </div>
 
@@ -2261,7 +2261,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es.html b/build/ems_es.html
index b88131a..ffc80ca 100644
--- a/build/ems_es.html
+++ b/build/ems_es.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1620,8 +1620,8 @@ Table of contents
 <li>PM 1</li>
 </ul>
 
-<details class="prereq" id="org28f38e1">
-<summary id="org4ff5949">
+<details class="prereq" id="org410047a">
+<summary id="orgaff4c90">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1629,8 +1629,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="org562fcf2">
-<summary id="org99ee0cc">
+<details class="objectives" id="org2aa623e">
+<summary id="org092779f">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1672,7 +1672,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_c.html b/build/ems_es_c.html
index 14958c4..38e637f 100644
--- a/build/ems_es_c.html
+++ b/build/ems_es_c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_c_cap.html b/build/ems_es_c_cap.html
index 23c5e85..fe67399 100644
--- a/build/ems_es_c_cap.html
+++ b/build/ems_es_c_cap.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,7 +1635,7 @@ C \equiv \frac{Q}{V}
 \]
 </p>
 
-<div class="example div" id="org1297454">
+<div class="example div" id="org8169eea">
 <p>
 <b>Concentric shells</b>
 </p>
@@ -1686,7 +1686,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_c_ic.html b/build/ems_es_c_ic.html
index d89f17a..c39af24 100644
--- a/build/ems_es_c_ic.html
+++ b/build/ems_es_c_ic.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1618,7 +1618,7 @@ Charge in hollow conductor.
 Induced surface charges on inside and outside surfaces.
 </p>
 
-<div class="example div" id="org0ce1dfe">
+<div class="example div" id="orgbfab016">
 <p>
 <b>Field outside spherical conductor with irregular cavity</b>
 </p>
@@ -1669,7 +1669,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_c_p.html b/build/ems_es_c_p.html
index 57d169f..45a477b 100644
--- a/build/ems_es_c_p.html
+++ b/build/ems_es_c_p.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1613,7 +1613,7 @@ Table of contents
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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 <div class="outline-text-5" id="text-ems_es_c_p">
-<div class="main div" id="org44b23ff">
+<div class="main div" id="org04f9e36">
 <p>
 <b>Basic Properties of a Conductor</b>
 </p>
@@ -1650,7 +1650,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_c_sc.html b/build/ems_es_c_sc.html
index 169bccc..2a2d45f 100644
--- a/build/ems_es_c_sc.html
+++ b/build/ems_es_c_sc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1618,14 +1618,14 @@ For a conductor, we can exploit the fact that electrical fields vanish on the in
 get a proper boundary condition for the potential.  Namely, here, boundary condition
 <a href="./ems_es_ep_bc.html#Edisc">Edisc</a> yields
 </p>
-<div class="eqlabel" id="orge4aa51f">
+<div class="eqlabel" id="orge79da84">
 <p>
 <a id="E_sur_cond"></a><a href="./ems_es_c_sc.html#E_sur_cond"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgbc9f5e5">
+<div class="alteqlabels" id="org1be8ec1">
 <ul class="org-ul">
 <li>Gr (2.48)</li>
 </ul>
@@ -1643,14 +1643,14 @@ get a proper boundary condition for the potential.  Namely, here, boundary condi
 <p>
 which in terms of potential reads
 </p>
-<div class="eqlabel" id="org4bb3570">
+<div class="eqlabel" id="org0a7e073">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org82a270e">
+<div class="alteqlabels" id="orgd2cade3">
 <ul class="org-ul">
 <li>Gr (2.49)</li>
 </ul>
@@ -1712,7 +1712,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_e.html b/build/ems_es_e.html
index f492c66..e71623a 100644
--- a/build/ems_es_e.html
+++ b/build/ems_es_e.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1634,14 +1634,14 @@ W_u = -\int_{{\bf a}}^{{\bf b}} {\bf E} \cdot d{\bf l}
 For a point charge distribution, the total work required to assemble it
 can also be rewritten in terms of the potential by using <a href="./ems_es_ep_d.html#p">p</a>,
 </p>
-<div class="eqlabel" id="org8f28b0d">
+<div class="eqlabel" id="orgc034eeb">
 <p>
 <a id="W_pcd"></a><a href="./ems_es_e.html#W_pcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7f0bee7">
+<div class="alteqlabels" id="orgb148868">
 <ul class="org-ul">
 <li>Gr (2.42)</li>
 </ul>
@@ -1660,14 +1660,14 @@ W = \frac{1}{2} \sum_{i=1}^m q_i \phi({\bf r}_i)
 For a volume charge distribution, this becomes
 </p>
 
-<div class="eqlabel" id="org8496249">
+<div class="eqlabel" id="orgb75a4ce">
 <p>
 <a id="W_vcd"></a><a href="./ems_es_e.html#W_vcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd44ae8e">
+<div class="alteqlabels" id="org9f114cc">
 <ul class="org-ul">
 <li>Gr (2.43)</li>
 </ul>
@@ -1709,14 +1709,14 @@ W = \frac{\varepsilon_0}{2} \left( \int_{\cal V} E^2 d\tau + \oint_{\cal S} \phi
 Integrating over all space (and thus dropping the surface integrale whose integrand is assumed
 to vanish at infinity), we get
 </p>
-<div class="eqlabel" id="org4f4c7f0">
+<div class="eqlabel" id="orgeb2ac20">
 <p>
 <a id="W_intEsq"></a><a href="./ems_es_e.html#W_intEsq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgeb19c6f">
+<div class="alteqlabels" id="orgb4e7763">
 <ul class="org-ul">
 <li>Gr (2.45)</li>
 </ul>
@@ -1724,7 +1724,7 @@ to vanish at infinity), we get
 </div>
 
 </div>
-<div class="core div" id="org61da001">
+<div class="core div" id="orgbef6240">
 <p>
 
 </p>
@@ -1738,7 +1738,7 @@ W = \frac{\varepsilon_0}{2} \int E^2 d\tau
 
 </div>
 
-<div class="example div" id="org84561d4">
+<div class="example div" id="org5ea2599">
 <p>
 <b>Energy of spherical shell</b>
 </p>
@@ -1811,7 +1811,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ec.html b/build/ems_es_ec.html
index cf9d228..afae1f1 100644
--- a/build/ems_es_ec.html
+++ b/build/ems_es_ec.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ec_b.html b/build/ems_es_ec_b.html
index 458100c..5f99d40 100644
--- a/build/ems_es_ec_b.html
+++ b/build/ems_es_ec_b.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ec_c.html b/build/ems_es_ec_c.html
index fa2d931..827c3b0 100644
--- a/build/ems_es_ec_c.html
+++ b/build/ems_es_ec_c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ec_q.html b/build/ems_es_ec_q.html
index 3ea49c9..ae53e39 100644
--- a/build/ems_es_ec_q.html
+++ b/build/ems_es_ec_q.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ec_s.html b/build/ems_es_ec_s.html
index f0de517..233ca08 100644
--- a/build/ems_es_ec_s.html
+++ b/build/ems_es_ec_s.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,7 +1635,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ef.html b/build/ems_es_ef.html
index db306f5..c6010c1 100644
--- a/build/ems_es_ef.html
+++ b/build/ems_es_ef.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ef_Gl.html b/build/ems_es_ef_Gl.html
index 6b90e43..dfc2e11 100644
--- a/build/ems_es_ef_Gl.html
+++ b/build/ems_es_ef_Gl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1658,14 +1658,14 @@ sphere of radius \(r\) around the charge,
 <p>
 so by superposition, we obtain
 </p>
-<div class="eqlabel" id="org91cf7d7">
+<div class="eqlabel" id="orgb8336e6">
 <p>
 <a id="Gl_i"></a><a href="./ems_es_ef_Gl.html#Gl_i"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6ea6288">
+<div class="alteqlabels" id="orgcbd1da6">
 <ul class="org-ul">
 <li>Gr (2.13)</li>
 </ul>
@@ -1673,7 +1673,7 @@ so by superposition, we obtain
 </div>
 
 </div>
-<div class="core div" id="org0decae8">
+<div class="core div" id="orgba40026">
 <p>
 <b>Gauss' law (in integral form)</b>
 </p>
@@ -1705,14 +1705,14 @@ By applying the divergence theorem,
 and using \(Q_{\mbox{enc}} = \int_{\cal V} \rho d\tau\),  and using the fact the the choice of volume
 is arbitrary, we get
 </p>
-<div class="eqlabel" id="org99cb3fa">
+<div class="eqlabel" id="org5b066f2">
 <p>
 <a id="Gl_d"></a><a href="./ems_es_ef_Gl.html#Gl_d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org26da670">
+<div class="alteqlabels" id="org392ac6d">
 <ul class="org-ul">
 <li>Gr (2.14)</li>
 </ul>
@@ -1720,7 +1720,7 @@ is arbitrary, we get
 </div>
 
 </div>
-<div class="core div" id="orga601c85">
+<div class="core div" id="orge1e429b">
 <p>
 <b>Gauss' law in differential form</b>
 </p>
@@ -1779,7 +1779,7 @@ cylindrical or plane symmetry.
 Gaussian surfaces:  respectively, concentric sphere, coaxial cylinder, pillbox.
 </p>
 
-<div class="example div" id="org5c01f30">
+<div class="example div" id="org0bb5eb9">
 <p>
 <a id="E_uni_sph"></a><a href="./ems_es_ef_Gl.html#E_uni_sph"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
@@ -1814,7 +1814,7 @@ Same as point charge at origin!
 
 </div>
 
-<div class="example div" id="org15c018b">
+<div class="example div" id="org3541fb3">
 <p>
 <b>Example 2.3</b>:  infinitely long cylinder carrying charge density \(\rho = k s\) for some constant \(k\). Find \({\bf E}\) within the cylinder.
 </p>
@@ -1853,7 +1853,7 @@ Therefore,
 </div>
 
 
-<div class="example div" id="org83647ca">
+<div class="example div" id="org803f9c7">
 <p>
 <b>Example 2.4</b>:  infinite plane (defined by \(z = 0\)) with uniform surface charge density \(\sigma\).  Find \({\bf E}\).
 </p>
@@ -1879,7 +1879,7 @@ where \(\hat{\bf n}\) is a unit vector extending away from the plane.  Independe
 
 </div>
 
-<div class="example div" id="org6d1758e">
+<div class="example div" id="orgda03843">
 <p>
 <b>Example 2.5</b>: two infinite planes (put them vertical) carrying equal but opposite uniform surface charge densities \(\pm \sigma\).
 </p>
@@ -1909,7 +1909,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ef_cE.html b/build/ems_es_ef_cE.html
index bfc48b6..6cf395a 100644
--- a/build/ems_es_ef_cE.html
+++ b/build/ems_es_ef_cE.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 Since the work done when moving on a closed path vanishes, we have
 </p>
 
-<div class="eqlabel" id="org2b0c542">
+<div class="eqlabel" id="org926bec2">
 <p>
 <a id="ointE0"></a><a href="./ems_es_ef_cE.html#ointE0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org02ac6b2">
+<div class="alteqlabels" id="org312e865">
 <ul class="org-ul">
 <li>Gr (2.19)</li>
 </ul>
@@ -1632,7 +1632,7 @@ Since the work done when moving on a closed path vanishes, we have
 </div>
 
 </div>
-<div class="core div" id="orga54176a">
+<div class="core div" id="org93e5f61">
 <p>
 
 </p>
@@ -1650,14 +1650,14 @@ Since the work done when moving on a closed path vanishes, we have
 which by <a href="./c_m_ic_stokes.html#Stokes">Stokes' theorem</a> implies that the electrostatic field is curlless,
 </p>
 
-<div class="eqlabel" id="orgd47b068">
+<div class="eqlabel" id="org6ca69db">
 <p>
 <a id="curlE0"></a><a href="./ems_es_ef_cE.html#curlE0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6235c0c">
+<div class="alteqlabels" id="orgf99cde0">
 <ul class="org-ul">
 <li>Gr (2.20)</li>
 </ul>
@@ -1665,7 +1665,7 @@ which by <a href="./c_m_ic_stokes.html#Stokes">Stokes' theorem</a> implies that
 </div>
 
 </div>
-<div class="core div" id="orgf1c6e91">
+<div class="core div" id="org6da5ea4">
 <p>
 
 </p>
@@ -1711,7 +1711,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ef_ccd.html b/build/ems_es_ef_ccd.html
index 3365b1c..67b6610 100644
--- a/build/ems_es_ef_ccd.html
+++ b/build/ems_es_ef_ccd.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1619,14 +1619,14 @@ calculated from Coulomb's law using the superposition principle.  Since each inf
 volume element \(d\tau' = dx' dy' dz'\) contains a charge \(dq' = \rho({\bf r}') d\tau'\), we have
 </p>
 
-<div class="eqlabel" id="org0685ec2">
+<div class="eqlabel" id="org9a902ae">
 <p>
 <a id="E_vcd"></a><a href="./ems_es_ef_ccd.html#E_vcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2a6f970">
+<div class="alteqlabels" id="org24bc1ed">
 <ul class="org-ul">
 <li>Gr4 (2.8)</li>
 </ul>
@@ -1634,7 +1634,7 @@ volume element \(d\tau' = dx' dy' dz'\) contains a charge \(dq' = \rho({\bf r}')
 </div>
 
 </div>
-<div class="main div" id="org6569d43">
+<div class="main div" id="orgbd6694b">
 <p>
 
 </p>
@@ -1654,14 +1654,14 @@ Similarly, if the charge is spread out over a two-dimensional surface \({\cal S}
 \(\sigma({\bf r})\), we have over an infinitesimal area \(da'\) a charge \(dq' = \sigma({\bf r}') da'\), so
 </p>
 
-<div class="eqlabel" id="org463d4a8">
+<div class="eqlabel" id="org8f319d9">
 <p>
 <a id="E_scd"></a><a href="./ems_es_ef_ccd.html#E_scd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1997b74">
+<div class="alteqlabels" id="orga69c955">
 <ul class="org-ul">
 <li>Gr4(2.7)</li>
 </ul>
@@ -1669,7 +1669,7 @@ Similarly, if the charge is spread out over a two-dimensional surface \({\cal S}
 </div>
 
 </div>
-<div class="main div" id="org0795fa2">
+<div class="main div" id="orgc2eeaf4">
 <p>
 
 </p>
@@ -1686,14 +1686,14 @@ Similarly, if the charge is spread out over a two-dimensional surface \({\cal S}
 Finally, for a line path \({\cal P}\) with linear charge density \(\lambda({\bf r}')\),
 </p>
 
-<div class="eqlabel" id="org5ea882d">
+<div class="eqlabel" id="org0bc767a">
 <p>
 <a id="E_lcd"></a><a href="./ems_es_ef_ccd.html#E_lcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org18ca9b1">
+<div class="alteqlabels" id="orgd0377cd">
 <ul class="org-ul">
 <li>Gr (2.6)</li>
 </ul>
@@ -1701,7 +1701,7 @@ Finally, for a line path \({\cal P}\) with linear charge density \(\lambda({\bf
 </div>
 
 </div>
-<div class="main div" id="org8e461ef">
+<div class="main div" id="org8983783">
 <p>
 
 </p>
@@ -1715,7 +1715,7 @@ Finally, for a line path \({\cal P}\) with linear charge density \(\lambda({\bf
 
 </div>
 
-<div class="example div" id="orge5b772b">
+<div class="example div" id="org71abbc9">
 <p>
 <b>Example</b>
 </p>
@@ -1749,7 +1749,7 @@ most easily by observing that \(\frac{d}{dx} \left( \frac{x}{\sqrt{z^2 + x^2}} \
   = \frac{1}{\sqrt{z^2 + x^2}} - \frac{x^2}{(z^2 + x^2)^{3/2}} = \frac{z^2}{(z^2 + x^2)^{3/2}}\),
 leading to
 </p>
-<aside id="org371c5b7">
+<aside id="orgc858d11">
 <p>
 You could alternately proceed by using changes of variables \(y = zx\) followed by \(y = \tanh \alpha\):
     \(\int_{-L}^L \frac{dx}{(z^2 + x^2)^{3/2}} = \frac{1}{z^2}
@@ -1806,7 +1806,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ef_pc.html b/build/ems_es_ef_pc.html
index 9869cce..f713e1f 100644
--- a/build/ems_es_ef_pc.html
+++ b/build/ems_es_ef_pc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1627,14 +1627,14 @@ an electric field originating from the source charge.
 Invoking the superposition principle, we can thus write
 </p>
 
-<div class="eqlabel" id="orge6e38f0">
+<div class="eqlabel" id="orgb20f3db">
 <p>
 <a id="FqE"></a><a href="./ems_es_ef_pc.html#FqE"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </p>
-<div class="alteqlabels" id="org066e788">
+<div class="alteqlabels" id="orgb9c95ac">
 <ul class="org-ul">
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 </ul>
@@ -1642,7 +1642,7 @@ Invoking the superposition principle, we can thus write
 </div>
 
 </div>
-<div class="core div" id="org171997a">
+<div class="core div" id="org2c433ed">
 <p>
 
 </p>
@@ -1658,14 +1658,14 @@ Invoking the superposition principle, we can thus write
 <p>
 with the electric field of a point charge distribution being
 </p>
-<div class="eqlabel" id="org87ef17e">
+<div class="eqlabel" id="org0f29d96">
 <p>
 <a id="E_pcd"></a><a href="./ems_es_ef_pc.html#E_pcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org2002a6f">
+<div class="alteqlabels" id="orga631b19">
 <ul class="org-ul">
 <li>Gr (2.4)</li>
 </ul>
@@ -1673,7 +1673,7 @@ with the electric field of a point charge distribution being
 </div>
 
 </div>
-<div class="core div" id="org38b7915">
+<div class="core div" id="orge8f31fb">
 <p>
 
 </p>
@@ -1691,7 +1691,7 @@ The electric field \({\bf E} ({\bf r})\) is thus the force per unit charge that
 be exerted if you put a test charge at position \({\bf r}\).
 </p>
 
-<div class="example div" id="org93d7f68">
+<div class="example div" id="org637a06b">
 <p>
 <b>Example</b>
 </p>
@@ -1735,7 +1735,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_efo.html b/build/ems_es_efo.html
index 686d4c7..69d5800 100644
--- a/build/ems_es_efo.html
+++ b/build/ems_es_efo.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1646,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_efo_cl.html b/build/ems_es_efo_cl.html
index 2cbf3a9..c765cad 100644
--- a/build/ems_es_efo_cl.html
+++ b/build/ems_es_efo_cl.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1619,14 +1619,14 @@ Table of contents
 <li>PM 1.4</li>
 </ul>
 
-<div class="eqlabel" id="orgcad778a">
+<div class="eqlabel" id="org873eb6a">
 <p>
 <a id="Cl"></a><a href="./ems_es_efo_cl.html#Cl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orge60882d">
+<div class="alteqlabels" id="org65f0463">
 <ul class="org-ul">
 <li>FLS II (4.9)</li>
 <li>Gr (2.1)</li>
@@ -1638,7 +1638,7 @@ Table of contents
 </div>
 
 </div>
-<div class="core div" id="org5f65836">
+<div class="core div" id="orgdcb1e5a">
 <p>
 The force \(F_{t\leftarrow s}\) exerted by a point source charge \(q_s\) sitting at \({\bf r}_s\)
 on a point test charge \(q_t\) sitting at \({\bf r}_t\) is given by Coulomb's law,
@@ -1655,7 +1655,7 @@ on a point test charge \(q_t\) sitting at \({\bf r}_t\) is given by Coulomb's la
 
 </div>
 
-<aside id="org82fc785">
+<aside id="org7a3b728">
 <p>
 In case you're wondering: the exact number in the denominator
 of the first equality is just \(4 \pi c^2\), so this equation really
@@ -1696,7 +1696,7 @@ in which \(\mu_0\) is the <b>vacuum permeability</b> (or alternately <i>permeabi
 with the <i>henry</i> \(H = kg~m^2 / s^2 A^2\) being the unit for inductance.
 </p>
 
-<div class="info div" id="org739c878">
+<div class="info div" id="org38aad0a">
 <p>
 <b>Info: the International System of Units</b>
 </p>
@@ -1753,7 +1753,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_efo_e.html b/build/ems_es_efo_e.html
index e5e9b9a..a99a32b 100644
--- a/build/ems_es_efo_e.html
+++ b/build/ems_es_efo_e.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1656,14 +1656,14 @@ For the path, the 'angular' part is not contributing (see drawings in
 FLS II 4-3). The integral is thus purely radial,
 </p>
 
-<div class="eqlabel" id="org1d38281">
+<div class="eqlabel" id="org656fdd9">
 <p>
 <a id="Wab"></a><a href="./ems_es_efo_e.html#Wab"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga342766">
+<div class="alteqlabels" id="org2c3b340">
 <ul class="org-ul">
 <li>Gr (2.18)</li>
 </ul>
@@ -1750,7 +1750,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_efo_exp.html b/build/ems_es_efo_exp.html
index e8730ae..7e5df4b 100644
--- a/build/ems_es_efo_exp.html
+++ b/build/ems_es_efo_exp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1615,17 +1615,17 @@ Table of contents
 <div class="outline-text-5" id="text-ems_es_efo_exp">
 </div>
 
-<div id="outline-container-org49d790a" class="outline-6">
-<h6 id="org49d790a"><a href="#org49d790a">Before Coulomb</a></h6>
+<div id="outline-container-org59b4e6b" class="outline-6">
+<h6 id="org59b4e6b"><a href="#org59b4e6b">Before Coulomb</a></h6>
 </div>
-<div id="outline-container-orgd713e5c" class="outline-6">
-<h6 id="orgd713e5c"><a href="#orgd713e5c">Cavendish's experiment</a></h6>
+<div id="outline-container-org3ab247a" class="outline-6">
+<h6 id="org3ab247a"><a href="#org3ab247a">Cavendish's experiment</a></h6>
 </div>
-<div id="outline-container-orga0bbfa0" class="outline-6">
-<h6 id="orga0bbfa0"><a href="#orga0bbfa0">Coulomb</a></h6>
+<div id="outline-container-org8896390" class="outline-6">
+<h6 id="org8896390"><a href="#org8896390">Coulomb</a></h6>
 </div>
-<div id="outline-container-org9f40a7a" class="outline-6">
-<h6 id="org9f40a7a"><a href="#org9f40a7a">Current status</a></h6>
+<div id="outline-container-org85b6259" class="outline-6">
+<h6 id="org85b6259"><a href="#org85b6259">Current status</a></h6>
 </div>
 </div>
 
@@ -1647,7 +1647,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_efo_ps.html b/build/ems_es_efo_ps.html
index 93b5b23..b121155 100644
--- a/build/ems_es_efo_ps.html
+++ b/build/ems_es_efo_ps.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1619,7 +1619,7 @@ Table of contents
 <li>PM 1.4</li>
 </ul>
 
-<div class="core div" id="org4c6f42c">
+<div class="core div" id="orga4833ac">
 <p>
 Electrical forces obey the <b>principle of superposition</b>:
 the electrostatic interaction between two charged particles is left entirely
@@ -1655,7 +1655,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep.html b/build/ems_es_ep.html
index 1fd28de..722b645 100644
--- a/build/ems_es_ep.html
+++ b/build/ems_es_ep.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1646,7 +1646,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep_PL.html b/build/ems_es_ep_PL.html
index e3d1c13..eb32c51 100644
--- a/build/ems_es_ep_PL.html
+++ b/build/ems_es_ep_PL.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1622,14 +1622,14 @@ Our two fundamental equations for the electrostatic field are
 \]
 For the electrostatic potential, by <a href="./ems_es_ep_fp.html#Emgp">Emgp</a>, Gauss's law becomes
 </p>
-<div class="eqlabel" id="orga248783">
+<div class="eqlabel" id="org2b4e2eb">
 <p>
 <a id="Poi"></a><a href="./ems_es_ep_PL.html#Poi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2e27297">
+<div class="alteqlabels" id="orgfd2b954">
 <ul class="org-ul">
 <li>Gr (2.24)</li>
 <li>PM (2.72)</li>
@@ -1638,7 +1638,7 @@ For the electrostatic potential, by <a href="./ems_es_ep_fp.html#Emgp">Emgp</a>,
 </div>
 
 </div>
-<div class="core div" id="org2b5be1d">
+<div class="core div" id="org36797b7">
 <p>
 <b>Poisson's equation</b>
 \[
@@ -1651,14 +1651,14 @@ For the electrostatic potential, by <a href="./ems_es_ep_fp.html#Emgp">Emgp</a>,
 <p>
 When the charge density vanishes, it becomes more simply
 </p>
-<div class="eqlabel" id="org98e969b">
+<div class="eqlabel" id="org97e70d7">
 <p>
 <a id="Lap"></a><a href="./ems_es_ep_PL.html#Lap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1b9ea13">
+<div class="alteqlabels" id="org5b0e4aa">
 <ul class="org-ul">
 <li>Gr (2.25)</li>
 <li>PM (2.75)</li>
@@ -1667,7 +1667,7 @@ When the charge density vanishes, it becomes more simply
 </div>
 
 </div>
-<div class="core div" id="orgdc0fc61">
+<div class="core div" id="org2470271">
 <p>
 <b>Laplace's Equation</b>
 \[
@@ -1703,7 +1703,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep_bc.html b/build/ems_es_ep_bc.html
index 2e0a3b3..0c208a1 100644
--- a/build/ems_es_ep_bc.html
+++ b/build/ems_es_ep_bc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1650,14 +1650,14 @@ applied to a small loop straddling the surface:
 <p>
 We can unify both boundary conditions into a  single equation:
 </p>
-<div class="eqlabel" id="org017eb44">
+<div class="eqlabel" id="orgd6777ab">
 <p>
 <a id="Edisc"></a><a href="./ems_es_ep_bc.html#Edisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5a5e4ce">
+<div class="alteqlabels" id="orgc09e9b8">
 <ul class="org-ul">
 <li>Gr (2.33)</li>
 </ul>
@@ -1692,14 +1692,14 @@ The gradient however inherits the discontinuity of the electrostatic field, sinc
 \]
 or
 </p>
-<div class="eqlabel" id="orge3f6c85">
+<div class="eqlabel" id="orgb49ce52">
 <p>
 <a id="dpdisc"></a><a href="./ems_es_ep_bc.html#dpdisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org2c83462">
+<div class="alteqlabels" id="orge2712a7">
 <ul class="org-ul">
 <li>Gr (2.36)</li>
 </ul>
@@ -1747,7 +1747,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep_d.html b/build/ems_es_ep_d.html
index f8ad046..a737c93 100644
--- a/build/ems_es_ep_d.html
+++ b/build/ems_es_ep_d.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1620,14 +1620,14 @@ field is independent of the path, and that it is proportional to the test charge
 We can thus define a function representing the work per unit charge and
 called the  <b>electrostatic potential</b>
 </p>
-<div class="eqlabel" id="org39ed3cc">
+<div class="eqlabel" id="orgdd07c9d">
 <p>
 <a id="p"></a><a href="./ems_es_ep_d.html#p"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgfc6116b">
+<div class="alteqlabels" id="orgf6a0d06">
 <ul class="org-ul">
 <li>Gr (2.21)</li>
 </ul>
@@ -1643,7 +1643,7 @@ called the  <b>electrostatic potential</b>
 \]
 </p>
 
-<aside id="org5587716">
+<aside id="orge62746e">
 <p>
 \(\phi\) carries as unit: Newton-meters per coulomb or joules per coulomb, which is called a <b>volt</b>.
 In the SI system where the ampere is a base unit, a volt is a \(kg m^2/s^3 A\).
@@ -1660,14 +1660,14 @@ want; it's energy <i>differences</i> which matter).
 The potential difference between two arbitrary points \({\bf a}\) and \({\bf b}\) is
 well-defined without the need to specify the reference point,
 </p>
-<div class="eqlabel" id="org63f500f">
+<div class="eqlabel" id="orgf67e56e">
 <p>
 <a id="p_diff"></a><a href="./ems_es_ep_d.html#p_diff"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org026dcd6">
+<div class="alteqlabels" id="orgb1d3baf">
 <ul class="org-ul">
 <li>Gr (2.21)</li>
 </ul>
@@ -1675,7 +1675,7 @@ well-defined without the need to specify the reference point,
 </div>
 
 </div>
-<div class="main div" id="orgf050485">
+<div class="main div" id="org25e0198">
 <p>
 \[
   \phi({\bf b}) - \phi({\bf a}) = - \int_{\bf a}^{\bf b} {\bf E} \cdot d{\bf l}
@@ -1692,14 +1692,14 @@ The reference point is typically put at infinity.  The electrostatic potential c
 point charge \(q\) at the origin can then be calculated (taking for convenience \(d{\bf l} = \hat{\bf r} dr\),
 <i>i.e.</i> moving in purely radially) as
 </p>
-<div class="eqlabel" id="orga100469">
+<div class="eqlabel" id="org67ee7aa">
 <p>
 <a id="p_pc"></a><a href="./ems_es_ep_d.html#p_pc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org83e9a3a">
+<div class="alteqlabels" id="orgea44f77">
 <ul class="org-ul">
 <li>FLS II (4.20,4.23)</li>
 <li>Gr (2.26)</li>
@@ -1722,14 +1722,14 @@ point charge \(q\) at the origin can then be calculated (taking for convenience
 The electrostatic potential moreover inherits the superposition principle from the electric field,
 so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we have
 </p>
-<div class="eqlabel" id="org8fb4f47">
+<div class="eqlabel" id="org5029ace">
 <p>
 <a id="p_pcd"></a><a href="./ems_es_ep_d.html#p_pcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd4b75d4">
+<div class="alteqlabels" id="org0cf45f4">
 <ul class="org-ul">
 <li>FLS II (4.24)</li>
 <li>Gr (2.27)</li>
@@ -1739,7 +1739,7 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
 </div>
 
 </div>
-<div class="core div" id="org0feaada">
+<div class="core div" id="orgc352918">
 <p>
 
 </p>
@@ -1755,14 +1755,14 @@ so for a distribution of point charges \(q_i\) at positions \({\bf r}_i\), we ha
 <p>
 For a continuous charge density in a volume \({\cal V}\), we have
 </p>
-<div class="eqlabel" id="org4f7acf1">
+<div class="eqlabel" id="org097c7ba">
 <p>
 <a id="p_vcd"></a><a href="./ems_es_ep_d.html#p_vcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org89a4a17">
+<div class="alteqlabels" id="orgadf3e61">
 <ul class="org-ul">
 <li>Gr (2.29)</li>
 <li>PM (2.18)</li>
@@ -1771,7 +1771,7 @@ For a continuous charge density in a volume \({\cal V}\), we have
 </div>
 
 </div>
-<div class="main div" id="orgce6daed">
+<div class="main div" id="org7057915">
 <p>
 
 </p>
@@ -1788,14 +1788,14 @@ For a continuous charge density in a volume \({\cal V}\), we have
 <p>
 whereas for a surface or line charge distribution, respectively,
 </p>
-<div class="eqlabel" id="orgcac3c57">
+<div class="eqlabel" id="org0e34443">
 <p>
 <a id="p_scd"></a><a href="./ems_es_ep_d.html#p_scd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5fbbe53">
+<div class="alteqlabels" id="orgbc8bb3d">
 <ul class="org-ul">
 <li>Gr (2.30)b</li>
 </ul>
@@ -1803,7 +1803,7 @@ whereas for a surface or line charge distribution, respectively,
 </div>
 
 </div>
-<div class="main div" id="org7d0d5f8">
+<div class="main div" id="org1212656">
 <p>
 \[
 \phi({\bf r}) = \frac{1}{4\pi \varepsilon_0} \int_{\cal S} da' \frac{\sigma({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1813,14 +1813,14 @@ whereas for a surface or line charge distribution, respectively,
 
 </div>
 
-<div class="eqlabel" id="org49407d6">
+<div class="eqlabel" id="org48a6015">
 <p>
 <a id="p_lcd"></a><a href="./ems_es_ep_d.html#p_lcd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgfd9b5c6">
+<div class="alteqlabels" id="orgbe2fc21">
 <ul class="org-ul">
 <li>Gr (2.30)a</li>
 </ul>
@@ -1828,7 +1828,7 @@ whereas for a surface or line charge distribution, respectively,
 </div>
 
 </div>
-<div class="main div" id="orgfc25e94">
+<div class="main div" id="org8e46f50">
 <p>
 
 </p>
@@ -1861,7 +1861,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep_ex.html b/build/ems_es_ep_ex.html
index d4609df..0dd8766 100644
--- a/build/ems_es_ep_ex.html
+++ b/build/ems_es_ep_ex.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1613,7 +1613,7 @@ Table of contents
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a><span class="headline-id">ems.es.ep.ex</span></h5>
 <div class="outline-text-5" id="text-ems_es_ep_ex">
-<div class="example div" id="orgcaa3290">
+<div class="example div" id="orga8633d3">
 <p>
 <b>Spherical shell: via \({\bf E}\)</b>
 </p>
@@ -1661,7 +1661,7 @@ and using spherical symmetry, we get:
 
 </div>
 
-<div class="example div" id="orgb08b399">
+<div class="example div" id="org9e191c6">
 <p>
 <b>Spherical shell: direct calculation</b>
 </p>
@@ -1738,7 +1738,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_es_ep_fp.html b/build/ems_es_ep_fp.html
index 7ad47af..3656f37 100644
--- a/build/ems_es_ep_fp.html
+++ b/build/ems_es_ep_fp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,14 +1639,14 @@ so
 <p>
 Since this is true for any choice of \({\bf a}\) and \({\bf b}\), we have
 </p>
-<div class="eqlabel" id="orgd7cc06c">
+<div class="eqlabel" id="org336e742">
 <p>
 <a id="Emgp"></a><a href="./ems_es_ep_fp.html#Emgp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org4f178ad">
+<div class="alteqlabels" id="orgbf39adb">
 <ul class="org-ul">
 <li>Gr (2.23)</li>
 </ul>
@@ -1654,7 +1654,7 @@ Since this is true for any choice of \({\bf a}\) and \({\bf b}\), we have
 </div>
 
 </div>
-<div class="core div" id="org07c0b3a">
+<div class="core div" id="orgf493e3f">
 <p>
 \[
 {\bf E} = -{\boldsymbol \nabla} \phi
@@ -1725,7 +1725,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms.html b/build/ems_ms.html
index fef5307..6895796 100644
--- a/build/ems_ms.html
+++ b/build/ems_ms.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1620,8 +1620,8 @@ Table of contents
 <li>PM 6</li>
 </ul>
 
-<details class="prereq" id="orge2c497a">
-<summary id="org76315f8">
+<details class="prereq" id="org8b4fefb">
+<summary id="org96c5f31">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1629,8 +1629,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="org1724943">
-<summary id="org51e4b43">
+<details class="objectives" id="orgab71bd2">
+<summary id="orgfa73a57">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1674,7 +1674,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_BS.html b/build/ems_ms_BS.html
index 7a13160..07a4cf0 100644
--- a/build/ems_ms_BS.html
+++ b/build/ems_ms_BS.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,18 +1617,18 @@ Table of contents
 The magnetic field issuing from a steady surrent
 is given experimentally (around 1820) by the
 </p>
-<div class="core div" id="orga827512">
+<div class="core div" id="org34aadaf">
 <p>
 <b>Biot-Savart law</b>
 </p>
-<div class="eqlabel" id="org52886c6">
+<div class="eqlabel" id="orge6e214c">
 <p>
 <a id="BiotSavart"></a><a href="./ems_ms_BS.html#BiotSavart"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgdc1e7ba">
+<div class="alteqlabels" id="org8fbcc6c">
 <ul class="org-ul">
 <li>FLS II (14.43)</li>
 <li>Gr (5.34)</li>
@@ -1658,15 +1658,15 @@ with the <i>henry</i> \(H = kg ~m^2 / s^2 A^2\) being the unit for inductance.
 <p>
 For surface and volume density currents:
 </p>
-<div class="main div" id="org7a35caa">
-<div class="eqlabel" id="org23a2575">
+<div class="main div" id="orgbda956e">
+<div class="eqlabel" id="org6fb688e">
 <p>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org85a286c">
+<div class="alteqlabels" id="orgee15b98">
 
 </div>
 
@@ -1677,14 +1677,14 @@ For surface and volume density currents:
 \tag{BiotSavart_s}\label{BiotSavart_s}
 \]
 </p>
-<div class="eqlabel" id="org938c8cc">
+<div class="eqlabel" id="org6b3b16a">
 <p>
 <a id="BiotSavart_v"></a><a href="./ems_ms_BS.html#BiotSavart_v"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd7e4616">
+<div class="alteqlabels" id="org9d91e81">
 
 </div>
 
@@ -1709,7 +1709,7 @@ The <b>superposition principle</b> applies here as well:  a collection of curren
 the vector sum of the fields generated by the individual currents.
 </p>
 
-<div class="example div" id="org01ad376">
+<div class="example div" id="org4f9c7fe">
 <p>
 <b>Example: \({\bf B}\) from long straight wire</b>
 </p>
@@ -1732,14 +1732,14 @@ B = \frac{\mu_0}{4\pi} I \int_{\theta_1}^{\theta_2} d\theta \cos \theta \frac{\c
 \]
 For infinite wire:  \(\theta_1 = -\pi/2\), \(\theta_2 = \pi/2\), so
 </p>
-<div class="eqlabel" id="org76e595d">
+<div class="eqlabel" id="org663b16d">
 <p>
 <a id="Bwire1"></a><a href="./ems_ms_BS.html#Bwire1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org1b67385">
+<div class="alteqlabels" id="orgbd6b387">
 <ul class="org-ul">
 <li>Gr (5.38)</li>
 </ul>
@@ -1768,7 +1768,7 @@ f = \frac{\mu_0}{2\pi} \frac{I_1 I_2}{d}
 (like currents attract).
 </p>
 
-<div class="example div" id="org961db5f">
+<div class="example div" id="org958b1a7">
 <p>
 <b>Example: \({\bf B}\) above a circular loop</b>
 </p>
@@ -1812,7 +1812,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_ce.html b/build/ems_ms_ce.html
index 769e916..77dbb5a 100644
--- a/build/ems_ms_ce.html
+++ b/build/ems_ms_ce.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,18 +1635,18 @@ through the surface is (minus) the change of charge contained inside the surface
 \]
 Since this is valid for any volume, we get the
 </p>
-<div class="core div" id="orga21a4ef">
+<div class="core div" id="org4acde67">
 <p>
 <b>Continuity Equation</b>
 </p>
-<div class="eqlabel" id="org32cd8f0">
+<div class="eqlabel" id="orgf83655d">
 <p>
 <a id="conteq"></a><a href="./ems_ms_ce.html#conteq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orged6767a">
+<div class="alteqlabels" id="orge613636">
 <ul class="org-ul">
 <li>FLS II (13.8)</li>
 <li>Gr (5.29)</li>
@@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_dcB.html b/build/ems_ms_dcB.html
index 059ae43..337d2c4 100644
--- a/build/ems_ms_dcB.html
+++ b/build/ems_ms_dcB.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_dcB_c.html b/build/ems_ms_dcB_c.html
index d431c14..fef51a8 100644
--- a/build/ems_ms_dcB_c.html
+++ b/build/ems_ms_dcB_c.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1663,18 +1663,18 @@ at infinity), and in the third step we have used the assumption of steady-state
 <p>
 We thus obtain
 </p>
-<div class="core div" id="org783256e">
+<div class="core div" id="orgea4bf7e">
 <p>
 <b>Ampère's law</b>
 </p>
-<div class="eqlabel" id="orge745f25">
+<div class="eqlabel" id="orgd432700">
 <p>
 <a id="Amp"></a><a href="./ems_ms_dcB_c.html#Amp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgda8539d">
+<div class="alteqlabels" id="org1527214">
 <ul class="org-ul">
 <li>FLS II (13.13)</li>
 <li>Gr (5.56)</li>
@@ -1699,18 +1699,18 @@ We thus obtain
 \]
 yielding
 </p>
-<div class="core div" id="org354b44c">
+<div class="core div" id="org47c2e9c">
 <p>
 <b>Ampère's law (integral form)</b>
 </p>
-<div class="eqlabel" id="orgd83eec1">
+<div class="eqlabel" id="org7d03160">
 <p>
 <a id="Amp_int"></a><a href="./ems_ms_dcB_c.html#Amp_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgfb58e7c">
+<div class="alteqlabels" id="org7df7f43">
 <ul class="org-ul">
 <li>FLS II (13.16)</li>
 <li>Gr (5.57)</li>
@@ -1741,7 +1741,7 @@ Sign ambiguity:  resolved by right-hand rule as usual.
 Ampère's law in magnetostatics takes a parallel role to Gauss's law in electrostatics.
 </p>
 
-<div class="example div" id="org228e2e4">
+<div class="example div" id="orgb588a5a">
 <p>
 <b>Example: infinite wire</b>
 </p>
@@ -1760,7 +1760,7 @@ choosing an amperian loop at a fixed radius \(r\), we get
 
 </div>
 
-<div class="example div" id="org6ded1ae">
+<div class="example div" id="orgdd3bf23">
 <p>
 <b>Example: uniform sheet current</b>
 </p>
@@ -1789,7 +1789,7 @@ and along \(\hat{\bf y}\) for \(z &lt; 0\).  Amperian loop of width \(l\) punchi
 
 </div>
 
-<div class="example div" id="org79e3791">
+<div class="example div" id="org620aee8">
 <p>
 <b>Example: solenoid</b>
 </p>
@@ -1809,14 +1809,14 @@ Outside:  infinitely far away, \({\bf B}\) must vanish.
 But an amperian loop outside gives zero always, so \({\bf B}\) vanishes everywhere outside the solenoid.
 Amperian loop of length \(l\), half-inside and half-outside:
 </p>
-<div class="eqlabel" id="orgca26b03">
+<div class="eqlabel" id="orgb28c666">
 <p>
 <a id="Bsol"></a><a href="./ems_ms_dcB_c.html#Bsol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc2fa23f">
+<div class="alteqlabels" id="orga2e2f32">
 <ul class="org-ul">
 <li>Gr (5.59)</li>
 </ul>
@@ -1841,7 +1841,7 @@ form of symmetry, for example
 i) infinite straight lines, ii) infinite planes, iii) infinite solenoids, iv) toroids.
 </p>
 
-<div class="example div" id="org0bb7ec0">
+<div class="example div" id="org4328fb9">
 <p>
 <b>Example: toroidal coil</b>
 </p>
@@ -1863,14 +1863,14 @@ Outside the coil, the field must again be zero.
 <p>
 Consider now an Amperian loop which is just a circle at radius \(r\):
 </p>
-<div class="eqlabel" id="orgbea10d8">
+<div class="eqlabel" id="orgf18763d">
 <p>
 <a id="Btor"></a><a href="./ems_ms_dcB_c.html#Btor"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8bc0f73">
+<div class="alteqlabels" id="orgd921abb">
 <ul class="org-ul">
 <li>Gr (5.60)</li>
 </ul>
@@ -1907,7 +1907,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_dcB_d.html b/build/ems_ms_dcB_d.html
index 3e00bab..48fdc87 100644
--- a/build/ems_ms_dcB_d.html
+++ b/build/ems_ms_dcB_d.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1642,15 +1642,15 @@ Note that we can write (using <a href="./c_m_dd_3d.html#div1or">div1or</a>) \(\f
 But \({\bf J}\) depends only on \({\bf r}'\) so \({\boldsymbol \nabla} \times {\bf J} ({\bf r}') = 0\), and since
 the curl of a gradient always vanishes, we obtain
 </p>
-<div class="core div" id="orgdba520c">
-<div class="eqlabel" id="orgd9bb35e">
+<div class="core div" id="orgef3d5dc">
+<div class="eqlabel" id="org1e13d7a">
 <p>
 <a id="divB0"></a><a href="./ems_ms_dcB_d.html#divB0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orge93ce7b">
+<div class="alteqlabels" id="org221b123">
 <ul class="org-ul">
 <li>FLS II (13.12)</li>
 <li>Gr (5.50)</li>
@@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_dcB_iw.html b/build/ems_ms_dcB_iw.html
index 634061c..39ebb3d 100644
--- a/build/ems_ms_dcB_iw.html
+++ b/build/ems_ms_dcB_iw.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 Let us start with the simple case of the field \({\bf B}\) coming from an infinite wire, as
 given by <a href="./ems_ms_BS.html#Bwire1">Bwire1</a>, rewritten here in cylindrical coordinates along the axis of the wire:
 </p>
-<div class="eqlabel" id="orgcbf3a0a">
+<div class="eqlabel" id="org3275cd1">
 <p>
 <a id="Bwire"></a><a href="./ems_ms_dcB_iw.html#Bwire"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7898995">
+<div class="alteqlabels" id="orgdc7fcb4">
 <ul class="org-ul">
 <li>Gr (5.39)</li>
 </ul>
@@ -1705,7 +1705,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_lf.html b/build/ems_ms_lf.html
index 809599f..cb6b65c 100644
--- a/build/ems_ms_lf.html
+++ b/build/ems_ms_lf.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_lf_pc.html b/build/ems_ms_lf_pc.html
index e88354d..94bbf79 100644
--- a/build/ems_ms_lf_pc.html
+++ b/build/ems_ms_lf_pc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,7 +1617,7 @@ Table of contents
 The magnetic force on a point charge \(q\) moving at velocity \({\bf v}\) in magnetic field \({\bf B}\)
 is given by
 </p>
-<div class="core div" id="org868db15">
+<div class="core div" id="org466d2d4">
 <p>
 \[
 {\bf F}_{mag} = q {\bf v} \times {\bf B}
@@ -1631,14 +1631,14 @@ Units of \({\bf B}\):  \(N/(A~m)\) is called a <b>tesla</b> (symbol: \(T\)).
 The total electromagnetic force on a point charge \(q\) moving at velocity
 \({\bf v}\) is given by the <b>Lorentz force</b>:
 </p>
-<div class="eqlabel" id="orga1b18db">
+<div class="eqlabel" id="org7610b82">
 <p>
 <a id="LorFo"></a><a href="./ems_ms_lf_pc.html#LorFo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb36876d">
+<div class="alteqlabels" id="orgb7f6718">
 <ul class="org-ul">
 <li>FLS II (13.1)</li>
 <li>Gr (5.2)</li>
@@ -1648,7 +1648,7 @@ The total electromagnetic force on a point charge \(q\) moving at velocity
 </div>
 
 </div>
-<div class="core div" id="org1cce15c">
+<div class="core div" id="orgc9794ed">
 <p>
 \[
 {\bf F} = q ({\bf E} + {\bf v} \times {\bf B})
@@ -1658,7 +1658,7 @@ The total electromagnetic force on a point charge \(q\) moving at velocity
 
 </div>
 
-<div class="example div" id="org45d1c2b">
+<div class="example div" id="orge0d0626">
 <p>
 <b>Cyclotron motion</b>
 </p>
@@ -1717,7 +1717,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_lf_sc.html b/build/ems_ms_lf_sc.html
index 561b5ad..250b4ff 100644
--- a/build/ems_ms_lf_sc.html
+++ b/build/ems_ms_lf_sc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1632,14 +1632,14 @@ This leads us to define a <b>current density</b> \({\bf J}\) as the vector repre
 charge flowing through a unit area per unit time, with direction along the motion of the charges.
 Then, \(\Delta q = \rho {\bf v} \cdot {\bf n} ~\Delta {\cal S} ~\Delta t\) so we can identify
 </p>
-<div class="eqlabel" id="org634eed3">
+<div class="eqlabel" id="org44135ba">
 <p>
 <a id="vcurd"></a><a href="./ems_ms_lf_sc.html#vcurd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgec85e6b">
+<div class="alteqlabels" id="org4e5f0fb">
 <ul class="org-ul">
 <li>Gr (5.26)</li>
 <li>PM (4.4)</li>
@@ -1659,14 +1659,14 @@ Then, \(\Delta q = \rho {\bf v} \cdot {\bf n} ~\Delta {\cal S} ~\Delta t\) so we
 Similarly, a current running down a wire can be described by a linear charge density \(\lambda\)
 moving at velocity \({\bf v}\), giving the current
 </p>
-<div class="eqlabel" id="orgb7eeef6">
+<div class="eqlabel" id="org1cfc3de">
 <p>
 <a id="lcurd"></a><a href="./ems_ms_lf_sc.html#lcurd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf8d5d1a">
+<div class="alteqlabels" id="org0236891">
 <ul class="org-ul">
 <li>Gr (5.14)</li>
 </ul>
@@ -1685,14 +1685,14 @@ moving at velocity \({\bf v}\), giving the current
 For charge flowing on a surface, we can describe the <b>surface current density</b> as a surface charge
 density \(\sigma\) moving at velocity \({\bf v}\),
 </p>
-<div class="eqlabel" id="org84167b3">
+<div class="eqlabel" id="org779b4e0">
 <p>
 <a id="scurd"></a><a href="./ems_ms_lf_sc.html#scurd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb6d5c96">
+<div class="alteqlabels" id="org6bb71f0">
 <ul class="org-ul">
 <li>Gr (5.23)</li>
 </ul>
@@ -1707,18 +1707,18 @@ density \(\sigma\) moving at velocity \({\bf v}\),
 \]
 </p>
 
-<div class="main div" id="org9ca056c">
+<div class="main div" id="org0a15fdb">
 <p>
 Magnetic forces on wire, surface and volume carrying current densities:
 </p>
-<div class="eqlabel" id="org92b3fea">
+<div class="eqlabel" id="orgefbcea9">
 <p>
 <a id="Fmagl"></a><a href="./ems_ms_lf_sc.html#Fmagl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgad8b186">
+<div class="alteqlabels" id="org2e3c12d">
 <ul class="org-ul">
 <li>Gr (5.16)</li>
 </ul>
@@ -1732,14 +1732,14 @@ Magnetic forces on wire, surface and volume carrying current densities:
 \tag{Fmagl}\label{Fmagl}
 \]
 </p>
-<div class="eqlabel" id="org5ab1162">
+<div class="eqlabel" id="orgd3c929c">
 <p>
 <a id="Fmags"></a><a href="./ems_ms_lf_sc.html#Fmags"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org5599c69">
+<div class="alteqlabels" id="orgd338de9">
 <ul class="org-ul">
 <li>Gr (5.24)</li>
 </ul>
@@ -1753,14 +1753,14 @@ Magnetic forces on wire, surface and volume carrying current densities:
 \tag{Fmags}\label{Fmags}
 \]
 </p>
-<div class="eqlabel" id="orgde4d414">
+<div class="eqlabel" id="org6a0eee5">
 <p>
 <a id="Fmagv"></a><a href="./ems_ms_lf_sc.html#Fmagv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org7f23ff0">
+<div class="alteqlabels" id="org79f6183">
 <ul class="org-ul">
 <li>Gr (5.27)</li>
 </ul>
@@ -1795,7 +1795,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp.html b/build/ems_ms_vp.html
index e335a38..b298b91 100644
--- a/build/ems_ms_vp.html
+++ b/build/ems_ms_vp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1641,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp_A.html b/build/ems_ms_vp_A.html
index 1876789..3804c7b 100644
--- a/build/ems_ms_vp_A.html
+++ b/build/ems_ms_vp_A.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,15 +1617,15 @@ Table of contents
 Since \({\boldsymbol \nabla} \cdot {\bf B} = 0\) in magnetostatics, following Helmholtz's theorem
 (see <a href="./c_m_vf_helm.html#c_m_vf_helm">c_m_vf_helm</a>) we can write
 </p>
-<div class="core div" id="org43892ce">
-<div class="eqlabel" id="org3a3bc3a">
+<div class="core div" id="org45049da">
+<div class="eqlabel" id="org453dd73">
 <p>
 <a id="BcurlA"></a><a href="./ems_ms_vp_A.html#BcurlA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb09d3b2">
+<div class="alteqlabels" id="orgec5b008">
 <ul class="org-ul">
 <li>Gr (5.61)</li>
 </ul>
@@ -1661,18 +1661,18 @@ add any curlless function (said otherwise: the gradient of any scalar field) to
 without changing the magnetic field.  Making a specific choice is called making a <b>gauge choice</b>.
 For example, we can always choose to eliminate the divergence of \({\bf A}\), giving us the example of the
 </p>
-<div class="main div" id="org6e595ac">
+<div class="main div" id="org052aa9f">
 <p>
 <b>Coulomb gauge</b>
 </p>
-<div class="eqlabel" id="orgff30682">
+<div class="eqlabel" id="org0d4e79a">
 <p>
 <a id="CoulG"></a><a href="./ems_ms_vp_A.html#CoulG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org9e044e6">
+<div class="alteqlabels" id="orgf4027ff">
 <ul class="org-ul">
 <li>Gr (5.63)</li>
 </ul>
@@ -1711,15 +1711,15 @@ zero at infinity,
 <p>
 Under this gauge choice, Ampère's law becomes
 </p>
-<div class="main div" id="org764e2b0">
-<div class="eqlabel" id="org3f693e5">
+<div class="main div" id="org0d3ac1c">
+<div class="eqlabel" id="orgf9b0e09">
 <p>
 <a id="Amp_CoulG"></a><a href="./ems_ms_vp_A.html#Amp_CoulG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org74208de">
+<div class="alteqlabels" id="org6421513">
 <ul class="org-ul">
 <li>Gr (5.64)</li>
 </ul>
@@ -1739,15 +1739,15 @@ Under this gauge choice, Ampère's law becomes
 Again this is precisely like the Poisson equation, with one separate equation for each component.
 For currents falling off sufficiently rapidly at infinity, we thus have
 </p>
-<div class="core div" id="orga51c6d0">
-<div class="eqlabel" id="orgf1fa3d4">
+<div class="core div" id="orgca4137c">
+<div class="eqlabel" id="org8edb89a">
 <p>
 <a id="A_CoulG"></a><a href="./ems_ms_vp_A.html#A_CoulG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org35d9537">
+<div class="alteqlabels" id="org9fe7761">
 <ul class="org-ul">
 <li>Gr (5.65)</li>
 </ul>
@@ -1766,15 +1766,15 @@ For currents falling off sufficiently rapidly at infinity, we thus have
 <p>
 For line and surface currents,
 </p>
-<div class="main div" id="org6da036c">
-<div class="eqlabel" id="orge6299eb">
+<div class="main div" id="orgdedfb57">
+<div class="eqlabel" id="orgb7bb9ef">
 <p>
 <a id="A_CoulG_l"></a><a href="./ems_ms_vp_A.html#A_CoulG_l"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga10cfa7">
+<div class="alteqlabels" id="org04f99f7">
 
 </div>
 
@@ -1785,14 +1785,14 @@ For line and surface currents,
 \tag{A_CoulG_l}\label{A_CoulG_l}
 \]
 </p>
-<div class="eqlabel" id="orgae969c5">
+<div class="eqlabel" id="org3d556f7">
 <p>
 <a id="A_CoulG_s"></a><a href="./ems_ms_vp_A.html#A_CoulG_s"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org3392659">
+<div class="alteqlabels" id="org5a752dc">
 
 </div>
 
@@ -1807,7 +1807,7 @@ For line and surface currents,
 </div>
 
 
-<div class="example div" id="org277d07b">
+<div class="example div" id="org71e8cc6">
 <p>
 <b>Example: infinite solenoid</b>
 </p>
@@ -1888,7 +1888,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp_LC.html b/build/ems_ms_vp_LC.html
index 5a37ebd..ddd4ede 100644
--- a/build/ems_ms_vp_LC.html
+++ b/build/ems_ms_vp_LC.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1618,18 +1618,18 @@ Similarly to the electrostatic dipole,
 the magnetic field of a dipole can be written in coordinate-free form.
 For this:  we define a useful object, the <br>
 </p>
-<div class="info div" id="org05a2609">
+<div class="info div" id="org049e396">
 <p>
 <b>Levi-Civita symbol</b>
 </p>
-<div class="eqlabel" id="orgce508dc">
+<div class="eqlabel" id="org194bb67">
 <p>
 <a id="LeviCivita"></a><a href="./ems_ms_vp_LC.html#LeviCivita"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org0208d2c">
+<div class="alteqlabels" id="org198e91f">
 
 </div>
 
@@ -1652,14 +1652,14 @@ Using this:  we can for example rewrite the cross product as
 \]
 Important identity:
 </p>
-<div class="eqlabel" id="org7163578">
+<div class="eqlabel" id="orgf21b17b">
 <p>
 <a id="sumLeviCivita"></a><a href="./ems_ms_vp_LC.html#sumLeviCivita"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgad94abf">
+<div class="alteqlabels" id="org7b851f6">
 
 </div>
 
@@ -1698,14 +1698,14 @@ and \(\epsilon_{ijk} \epsilon_{klm} = \epsilon_{ijk} \epsilon_{lmk} = \delta_{il
 <p>
 Putting back the vector notation, and the \(m\) notation for the magnetic dipole (instead of \(M\)), we obtain
 </p>
-<div class="eqlabel" id="org8d308be">
+<div class="eqlabel" id="org6cbce3c">
 <p>
 <a id="B_di"></a><a href="./ems_ms_vp_LC.html#B_di"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org51c2391">
+<div class="alteqlabels" id="orgaf52e02">
 <ul class="org-ul">
 <li>Gr (5.89)</li>
 </ul>
@@ -1743,7 +1743,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp_comp.html b/build/ems_ms_vp_comp.html
index e0633df..78847b2 100644
--- a/build/ems_ms_vp_comp.html
+++ b/build/ems_ms_vp_comp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1683,7 +1683,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp_mbc.html b/build/ems_ms_vp_mbc.html
index fc1a741..4e82ca9 100644
--- a/build/ems_ms_vp_mbc.html
+++ b/build/ems_ms_vp_mbc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1649,15 +1649,15 @@ B^{\parallel}_{above} - B^{\parallel}_{below} = \mu_0 K
 Thus, the component of \({\bf B}\) that is parallel to surface but perpendicular to the current flow
 is discontinuous, whereas the one parallel to the flow is continuous.  In vector notation, this becomes
 </p>
-<div class="main div" id="org12d7a29">
-<div class="eqlabel" id="org788cf9f">
+<div class="main div" id="orgd7c3fd5">
+<div class="eqlabel" id="org969d04f">
 <p>
 <a id="Bdisc"></a><a href="./ems_ms_vp_mbc.html#Bdisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgce8ac7d">
+<div class="alteqlabels" id="org3925adb">
 <ul class="org-ul">
 <li>Gr (5.76)</li>
 </ul>
@@ -1676,15 +1676,15 @@ is discontinuous, whereas the one parallel to the flow is continuous.  In vector
 <p>
 where \(\hat{\bf n}\) points upwards. For the vector potential, the relations are
 </p>
-<div class="main div" id="org98afe60">
-<div class="eqlabel" id="org1152f89">
+<div class="main div" id="orgaa8e0a4">
+<div class="eqlabel" id="orgdb6012c">
 <p>
 <a id="Adisc"></a><a href="./ems_ms_vp_mbc.html#Adisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgacd4a93">
+<div class="alteqlabels" id="orgcdbc2a6">
 <ul class="org-ul">
 <li>Gr (5.77)</li>
 </ul>
@@ -1737,15 +1737,15 @@ What is left is
 \]
 Therefore, reidentifying the normal component, we get
 </p>
-<div class="main div" id="orgcfe3f01">
-<div class="eqlabel" id="org11b9194">
+<div class="main div" id="orgd2b01f8">
+<div class="eqlabel" id="org9b12626">
 <p>
 <a id="dAdisc"></a><a href="./ems_ms_vp_mbc.html#dAdisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org41f86e1">
+<div class="alteqlabels" id="org0315d9a">
 <ul class="org-ul">
 <li>Gr (5.78)</li>
 </ul>
@@ -1782,7 +1782,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/ems_ms_vp_me.html b/build/ems_ms_vp_me.html
index 4c68607..a79e79c 100644
--- a/build/ems_ms_vp_me.html
+++ b/build/ems_ms_vp_me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1629,14 +1629,14 @@ can thus be written
 \]
 Explicitly, the first few terms are (letting \(\hat{\bf r} \cdot \hat{\bf r}_s = \cos \theta\))
 </p>
-<div class="eqlabel" id="org5130ba2">
+<div class="eqlabel" id="org9991a67">
 <p>
 <a id="A_Leg"></a><a href="./ems_ms_vp_me.html#A_Leg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org4bcf6bb">
+<div class="alteqlabels" id="org70670d3">
 <ul class="org-ul">
 <li>Gr (5.80)</li>
 </ul>
@@ -1663,14 +1663,14 @@ monopoles (also from Maxwell's equation <a href="./ems_ms_dcB_d.html#divB0">divB
 <p>
 The dominant term is thus the dipole,
 </p>
-<div class="eqlabel" id="orgba02679">
+<div class="eqlabel" id="org6ae2775">
 <p>
 <a id="A_di1"></a><a href="./ems_ms_vp_me.html#A_di1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orga27ade1">
+<div class="alteqlabels" id="org46c3ea1">
 <ul class="org-ul">
 <li>Gr (5.85)</li>
 </ul>
@@ -1685,14 +1685,14 @@ The dominant term is thus the dipole,
 \]
 Using the identity (see Gr Problem 1.62),
 </p>
-<div class="eqlabel" id="org3f6dca3">
+<div class="eqlabel" id="orgcbd4b12">
 <p>
 <a id="intcr"></a><a href="./ems_ms_vp_me.html#intcr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orge0834a1">
+<div class="alteqlabels" id="orgf8baea5">
 <ul class="org-ul">
 <li>Gr (1.108)</li>
 </ul>
@@ -1709,7 +1709,7 @@ Using the identity (see Gr Problem 1.62),
 with \({\bf c} = \hat {\bf r}\),
 </p>
 
-<div class="info div" id="org04c6a44">
+<div class="info div" id="org099b0fe">
 <p>
 <b>Parenthesis:  derivation of</b> <a href="./ems_ms_vp_me.html#intcr">intcr</a>
 </p>
@@ -1752,18 +1752,18 @@ Back to our problem:
 \]
 and defining the
 </p>
-<div class="core div" id="orgbe06c08">
+<div class="core div" id="org11ff67d">
 <p>
 <b>magnetic dipole moment</b>
 </p>
-<div class="eqlabel" id="orgdd422db">
+<div class="eqlabel" id="orgcaf0476">
 <p>
 <a id="magdim"></a><a href="./ems_ms_vp_me.html#magdim"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6cd583f">
+<div class="alteqlabels" id="org2f58487">
 <ul class="org-ul">
 <li>Gr (5.86)</li>
 </ul>
@@ -1782,18 +1782,18 @@ and defining the
 <p>
 we obtain the convenient expression for the
 </p>
-<div class="main div" id="org066e08b">
+<div class="main div" id="orgaf2f07b">
 <p>
 <b>dipole term of the vector potential</b>
 </p>
-<div class="eqlabel" id="org7c02396">
+<div class="eqlabel" id="org9e396b0">
 <p>
 <a id="A_di"></a><a href="./ems_ms_vp_me.html#A_di"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf4eddbd">
+<div class="alteqlabels" id="orge4aef58">
 <ul class="org-ul">
 <li>Gr (5.85)</li>
 </ul>
@@ -1810,7 +1810,7 @@ we obtain the convenient expression for the
 
 </div>
 
-<div class="example div" id="org70776ed">
+<div class="example div" id="orge5a4d71">
 <p>
 <b>Example: bookend shape</b>
 </p>
@@ -1864,7 +1864,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm.html b/build/emsm.html
index cfc8d2f..b6439dd 100644
--- a/build/emsm.html
+++ b/build/emsm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emsm</span></h2>
 
 <div class="outline-text-2" id="text-emsm">
-<details class="prereq" id="org013ef1b">
-<summary id="orgdf86daf">
+<details class="prereq" id="org2cdb29a">
+<summary id="org9059216">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1624,8 +1624,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="org6f330fd">
-<summary id="org5ce87ab">
+<details class="objectives" id="orgde89868">
+<summary id="orge85578f">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1663,7 +1663,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm.html b/build/emsm_esm.html
index f1f7963..bbf6ff0 100644
--- a/build/emsm_esm.html
+++ b/build/emsm_esm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1641,7 +1641,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_D.html b/build/emsm_esm_D.html
index 73c1bce..bb66ba4 100644
--- a/build/emsm_esm_D.html
+++ b/build/emsm_esm_D.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,7 +1617,7 @@ Table of contents
 <p>
 Field due to polarization:  effectively comes from bound surface and volume charges,
 </p>
-<div class="main div" id="orgadd4b69">
+<div class="main div" id="org3baf02c">
 <p>
 \[
     \rho_b = -{\boldsymbol \nabla} \cdot {\bf P}, \hspace{1cm} \sigma_b = {\bf P} \cdot \hat{\bf n}.
@@ -1646,18 +1646,18 @@ Convenient way of writing:
 \]
 Defining the
 </p>
-<div class="core div" id="org1bfbe0c">
+<div class="core div" id="org16f838c">
 <p>
 <b>Electric displacement</b> \({\bf D}\)
 </p>
-<div class="eqlabel" id="orgadf914a">
+<div class="eqlabel" id="org3523024">
 <p>
 <a id="D"></a><a href="./emsm_esm_D.html#D"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org289b58b">
+<div class="alteqlabels" id="org6db7477">
 <ul class="org-ul">
 <li>Gr (4.21)</li>
 </ul>
@@ -1676,15 +1676,15 @@ Defining the
 <p>
 Gauss's law becomes
 </p>
-<div class="core div" id="org3c3599d">
-<div class="eqlabel" id="org5565708">
+<div class="core div" id="org054be1d">
+<div class="eqlabel" id="orgddc2c4a">
 <p>
 <a id="GlD"></a><a href="./emsm_esm_D.html#GlD"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org06803ca">
+<div class="alteqlabels" id="orgc397468">
 <ul class="org-ul">
 <li>Gr (4.22)</li>
 </ul>
@@ -1703,15 +1703,15 @@ Gauss's law becomes
 <p>
 or in integral form
 </p>
-<div class="core div" id="org81fd8e3">
-<div class="eqlabel" id="org6289c7f">
+<div class="core div" id="org3b41507">
+<div class="eqlabel" id="orgc0985b4">
 <p>
 <a id="GlD_int"></a><a href="./emsm_esm_D.html#GlD_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org0d6b00c">
+<div class="alteqlabels" id="org05b98c1">
 <ul class="org-ul">
 <li>Gr (4.23)</li>
 </ul>
@@ -1728,7 +1728,7 @@ or in integral form
 
 </div>
 
-<div class="example div" id="orge0e4a91">
+<div class="example div" id="org1cba48b">
 <p>
 <b>Example: long insulated wire</b>
 </p>
@@ -1773,14 +1773,14 @@ Inside:  can't know the electric field, since \({\bf P}\) isn't known.
 but this is <i>not</i> correct, because the curl of the displacement isn't necessarily zero,
 </p>
 
-<div class="eqlabel" id="orgb86dac9">
+<div class="eqlabel" id="org1af1759">
 <p>
 <a id="curlDcurlP"></a><a href="./emsm_esm_D.html#curlDcurlP"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6510384">
+<div class="alteqlabels" id="org40f1f22">
 <ul class="org-ul">
 <li>Gr (4.25)</li>
 </ul>
@@ -1820,7 +1820,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_D_bc.html b/build/emsm_esm_D_bc.html
index ace3b86..2110203 100644
--- a/build/emsm_esm_D_bc.html
+++ b/build/emsm_esm_D_bc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,14 +1616,14 @@ Table of contents
 <p>
 From <a href="./emsm_esm_D.html#GlD_int">GlD_int</a>, using the usual Gaussian pillbox logic:
 </p>
-<div class="eqlabel" id="org8ff3eb0">
+<div class="eqlabel" id="orgbdcee2a">
 <p>
 <a id="Dperp_disc"></a><a href="./emsm_esm_D_bc.html#Dperp_disc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org338781a">
+<div class="alteqlabels" id="org4320713">
 <ul class="org-ul">
 <li>Gr (4.26)</li>
 </ul>
@@ -1638,15 +1638,15 @@ D^{\perp}_{above} - D^{\perp}_{below} = \sigma_f
 \]
 Then, <a href="./emsm_esm_D.html#curlDcurlP">curlDcurlP</a> gives
 </p>
-<div class="main div" id="org5bce686">
-<div class="eqlabel" id="org278337e">
+<div class="main div" id="org7f57689">
+<div class="eqlabel" id="org047e623">
 <p>
 <a id="Dpar_disc"></a><a href="./emsm_esm_D_bc.html#Dpar_disc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgeca80db">
+<div class="alteqlabels" id="org53d514f">
 <ul class="org-ul">
 <li>Gr (4.27)</li>
 </ul>
@@ -1681,7 +1681,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_di.html b/build/emsm_esm_di.html
index fc0b8ef..4565d8f 100644
--- a/build/emsm_esm_di.html
+++ b/build/emsm_esm_di.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1648,7 +1648,7 @@ This is common in crystals, leading to phenomena such as double refraction.
 the dielectric are independent of the direction of \({\bf E}\) (isotropy).  Liquids fall into
 this category.  We here have
 </p>
-<div class="main div" id="org31ece11">
+<div class="main div" id="orge5de496">
 <p>
 \[
 {\bf P} = \varepsilon_0 \chi_e {\bf E}
@@ -1677,7 +1677,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_ld.html b/build/emsm_esm_ld.html
index d927b2f..908a641 100644
--- a/build/emsm_esm_ld.html
+++ b/build/emsm_esm_ld.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_ld_bvp.html b/build/emsm_esm_ld_bvp.html
index 4e43212..0d6306f 100644
--- a/build/emsm_esm_ld_bvp.html
+++ b/build/emsm_esm_ld_bvp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 In homogeneous linear dielectric, the bound charge density is directly
 proportional to the free charge:
 </p>
-<div class="eqlabel" id="org5a60e41">
+<div class="eqlabel" id="org3b1faf3">
 <p>
 <a id="rhob_ld"></a><a href="./emsm_esm_ld_bvp.html#rhob_ld"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf2e150e">
+<div class="alteqlabels" id="org1fe40e5">
 <ul class="org-ul">
 <li>Gr (4.39)</li>
 </ul>
@@ -1646,15 +1646,15 @@ and the potential then obeys the Laplace equation.
 It is convenient to rewrite our boundary conditions in terms of free charge densities:
 from <a href="./emsm_esm_D_bc.html#Dperp_disc">Dperp_disc</a>,
 </p>
-<div class="main div" id="orgf7ac2ac">
-<div class="eqlabel" id="org15ad919">
+<div class="main div" id="org1043649">
+<div class="eqlabel" id="org768d5d8">
 <p>
 <a id="Edisc_f"></a><a href="./emsm_esm_ld_bvp.html#Edisc_f"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2eadaf5">
+<div class="alteqlabels" id="orgb833c08">
 <ul class="org-ul">
 <li>Gr (4.40)</li>
 </ul>
@@ -1673,15 +1673,15 @@ from <a href="./emsm_esm_D_bc.html#Dperp_disc">Dperp_disc</a>,
 <p>
 or in terms of the potential,
 </p>
-<div class="main div" id="org6b3545e">
-<div class="eqlabel" id="org2ef4740">
+<div class="main div" id="orgd7fd379">
+<div class="eqlabel" id="orgcd8da1d">
 <p>
 <a id="dpdisc_f"></a><a href="./emsm_esm_ld_bvp.html#dpdisc_f"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd5ad929">
+<div class="alteqlabels" id="org49e04f7">
 <ul class="org-ul">
 <li>Gr (4.41)</li>
 </ul>
@@ -1701,15 +1701,15 @@ or in terms of the potential,
 <p>
 The potential itself is continuous,
 </p>
-<div class="main div" id="org3ca662e">
-<div class="eqlabel" id="org833e744">
+<div class="main div" id="orged360ff">
+<div class="eqlabel" id="orgee30116">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org27d0122">
+<div class="alteqlabels" id="orgb06a000">
 <ul class="org-ul">
 <li>Gr (4.42)</li>
 </ul>
@@ -1727,7 +1727,7 @@ The potential itself is continuous,
 </div>
 
 
-<div class="example div" id="org34078f8">
+<div class="example div" id="org9c5f579">
 <p>
 <b>Example: sphere of homogeneous dielectric material in uniform electric field</b>
 </p>
@@ -1794,7 +1794,7 @@ Thus,
 </div>
 
 
-<div class="example div" id="orgbbf1e7e">
+<div class="example div" id="org8809f63">
 <p>
 <b>Example: point charge above dielectric plane</b>
 </p>
@@ -1876,7 +1876,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_ld_e.html b/build/emsm_esm_ld_e.html
index 0440168..4389a84 100644
--- a/build/emsm_esm_ld_e.html
+++ b/build/emsm_esm_ld_e.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1659,15 +1659,15 @@ Special case of linear isotropic dielectric:  \({\bf D} = \varepsilon {\bf E}\),
 \]
 Total work done:
 </p>
-<div class="main div" id="org80ef55b">
-<div class="eqlabel" id="org713a49e">
+<div class="main div" id="orge697b0d">
+<div class="eqlabel" id="org3d3cbf1">
 <p>
 <a id="WintDE"></a><a href="./emsm_esm_ld_e.html#WintDE"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org23ade8c">
+<div class="alteqlabels" id="orgaa9054c">
 <ul class="org-ul">
 <li>Gr (4.58)</li>
 </ul>
@@ -1704,7 +1704,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_ld_f.html b/build/emsm_esm_ld_f.html
index ae60515..0c59b7f 100644
--- a/build/emsm_esm_ld_f.html
+++ b/build/emsm_esm_ld_f.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,14 +1637,14 @@ F = -\frac{dW}{dx}
 \]
 Energy stored in capacitor:
 </p>
-<div class="eqlabel" id="org8800210">
+<div class="eqlabel" id="org058bb27">
 <p>
 <a id="WcapV"></a><a href="./emsm_esm_ld_f.html#WcapV"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org812fe97">
+<div class="alteqlabels" id="org07c1712">
 <ul class="org-ul">
 <li>Gr (4.61)</li>
 </ul>
@@ -1667,14 +1667,14 @@ C = \frac{\varepsilon_0 w}{d} (\varepsilon_r l - \chi_e x)
 where \(l\) is the length of the plates, and \(w\) is their width.  Assume total charge \(Q\) on each
 plate is held constant as \(x\) changes.  In terms of \(Q\),
 </p>
-<div class="eqlabel" id="orgb61bde4">
+<div class="eqlabel" id="orgf7d01ba">
 <p>
 <a id="WcapQ"></a><a href="./emsm_esm_ld_f.html#WcapQ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org312899c">
+<div class="alteqlabels" id="org8ca789f">
 <ul class="org-ul">
 <li>Gr (4.63)</li>
 </ul>
@@ -1748,7 +1748,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_ld_sp.html b/build/emsm_esm_ld_sp.html
index 1401dcd..46a3466 100644
--- a/build/emsm_esm_ld_sp.html
+++ b/build/emsm_esm_ld_sp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,15 +1616,15 @@ Table of contents
 <p>
 For many substances:  polarization is proportional to field, at least if the latter isn't too strong:
 </p>
-<div class="main div" id="orgca50808">
-<div class="eqlabel" id="org6b1486e">
+<div class="main div" id="org918205a">
+<div class="eqlabel" id="org76e0bb4">
 <p>
 <a id="PchiE"></a><a href="./emsm_esm_ld_sp.html#PchiE"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org0fb5cad">
+<div class="alteqlabels" id="org15f84a2">
 <ul class="org-ul">
 <li>Gr (4.30)</li>
 </ul>
@@ -1661,15 +1661,15 @@ In linear dielectrics:
 \]
 so
 </p>
-<div class="main div" id="orgac075e9">
-<div class="eqlabel" id="orge6ef08e">
+<div class="main div" id="org4bf8e19">
+<div class="eqlabel" id="org8eba014">
 <p>
 <a id="DepsE"></a><a href="./emsm_esm_ld_sp.html#DepsE"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd3687f6">
+<div class="alteqlabels" id="org6d6db57">
 <ul class="org-ul">
 <li>Gr (4.32)</li>
 </ul>
@@ -1690,14 +1690,14 @@ where \(\varepsilon\) is called the <b>permittivity</b> of the material.
 In vacuum, susceptibility is zero,
 permittivity is \(\varepsilon_0\).  Also,
 </p>
-<div class="eqlabel" id="org7b81d68">
+<div class="eqlabel" id="org44480e1">
 <p>
 <a id="epsr"></a><a href="./emsm_esm_ld_sp.html#epsr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd11960a">
+<div class="alteqlabels" id="org820fcc3">
 <ul class="org-ul">
 <li>Gr (4.34)</li>
 </ul>
@@ -1716,7 +1716,7 @@ This is all just nomenclature, everything is already in <a href="./emsm_esm_ld_s
 
 
 
-<div class="example div" id="org94c117c">
+<div class="example div" id="org96b31be">
 <p>
 <b>Example: metal sphere with insulator shell</b>
 </p>
@@ -1790,7 +1790,7 @@ entirely filled with a homogeneous linear dielectric, but then this is just like
 a vacuum with a different permittivity.
 </p>
 
-<div class="example div" id="org9b0a9fc">
+<div class="example div" id="orgf706821">
 <p>
 <b>Example: parallel-plate capacitor filled with dielectric material</b>
 </p>
@@ -1839,7 +1839,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_mE.html b/build/emsm_esm_mE.html
index 6e34083..46597f3 100644
--- a/build/emsm_esm_mE.html
+++ b/build/emsm_esm_mE.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_mE_P.html b/build/emsm_esm_mE_P.html
index de0c9d1..4ef9a51 100644
--- a/build/emsm_esm_mE_P.html
+++ b/build/emsm_esm_mE_P.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1645,7 +1645,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_mE_o.html b/build/emsm_esm_mE_o.html
index 144c193..e62c992 100644
--- a/build/emsm_esm_mE_o.html
+++ b/build/emsm_esm_mE_o.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1695,18 +1695,18 @@ dipole moment pointing from \(O^-\) along bisector.
 <p>
 Torque on dipole:  if field is uniform, overall force on dipole cancels, but torque remains:
 </p>
-<div class="main div" id="orgfb793ed">
+<div class="main div" id="org6d38e7c">
 <p>
 <b>Torque on a dipole</b>
 </p>
-<div class="eqlabel" id="org697cf52">
+<div class="eqlabel" id="orgb18a402">
 <p>
 <a id="di_N"></a><a href="./emsm_esm_mE_o.html#di_N"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org4d4be74">
+<div class="alteqlabels" id="org4b4b4c6">
 <ul class="org-ul">
 <li>Gr (4.4)</li>
 </ul>
@@ -1729,15 +1729,15 @@ If field is non-uniform,
 \]
 so
 </p>
-<div class="main div" id="org035b61e">
-<div class="eqlabel" id="org4d19e6c">
+<div class="main div" id="org4892956">
+<div class="eqlabel" id="org74eee3a">
 <p>
 <a id="di_F"></a><a href="./emsm_esm_mE_o.html#di_F"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2c810a1">
+<div class="alteqlabels" id="org2419d6c">
 <ul class="org-ul">
 <li>Gr (4.5)</li>
 </ul>
@@ -1756,14 +1756,14 @@ so
 <p>
 The energy of a dipole in an electric field can be shown to be
 </p>
-<div class="eqlabel" id="org17f8e9c">
+<div class="eqlabel" id="org6beaaad">
 <p>
 <a id="di_E"></a><a href="./emsm_esm_mE_o.html#di_E"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org79b39b0">
+<div class="alteqlabels" id="org1930f1b">
 <ul class="org-ul">
 <li>Gr (4.6)</li>
 </ul>
@@ -1816,7 +1816,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_po.html b/build/emsm_esm_po.html
index 2a6c0c3..dfbbebb 100644
--- a/build/emsm_esm_po.html
+++ b/build/emsm_esm_po.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1624,14 +1624,14 @@ For a single dipole, we have <a href="./ems_ca_me_md.html#p_di">p_di</a>
 \]
 Considering a dipole moment per unit volume \({\bf P}\) (our definition of the polarization), we get
 </p>
-<div class="eqlabel" id="org0258040">
+<div class="eqlabel" id="orgf9d8b73">
 <p>
 <a id="p_P"></a><a href="./emsm_esm_po.html#p_P"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf8823e1">
+<div class="alteqlabels" id="org0d6708a">
 <ul class="org-ul">
 <li>Gr (4.9)</li>
 </ul>
@@ -1666,15 +1666,15 @@ Using the divergence theorem, this becomes
 <p>
 Interpretation:  first terms is like contribution of a surface charge,
 </p>
-<div class="main div" id="org0d67ad6">
-<div class="eqlabel" id="org6822ee4">
+<div class="main div" id="orgda7ad07">
+<div class="eqlabel" id="orgb0c539d">
 <p>
 <a id="sigmab"></a><a href="./emsm_esm_po.html#sigmab"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf05f86c">
+<div class="alteqlabels" id="org470a253">
 <ul class="org-ul">
 <li>Gr (4.11)</li>
 </ul>
@@ -1693,15 +1693,15 @@ Interpretation:  first terms is like contribution of a surface charge,
 <p>
 and second term looks like contribution of a volume charge,
 </p>
-<div class="main div" id="org6d35d8a">
-<div class="eqlabel" id="org869cfc2">
+<div class="main div" id="org2fcf5d5">
+<div class="eqlabel" id="org236705d">
 <p>
 <a id="rhob"></a><a href="./emsm_esm_po.html#rhob"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org0b847eb">
+<div class="alteqlabels" id="orgfa342f9">
 <ul class="org-ul">
 <li>Gr (4.12)</li>
 </ul>
@@ -1720,15 +1720,15 @@ and second term looks like contribution of a volume charge,
 <p>
 Using these definitions,
 </p>
-<div class="main div" id="org8829df8">
-<div class="eqlabel" id="orgd8388a5">
+<div class="main div" id="org52f84a1">
+<div class="eqlabel" id="org6d08561">
 <p>
 <a id="p_bound"></a><a href="./emsm_esm_po.html#p_bound"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org2103784">
+<div class="alteqlabels" id="orgb8910a7">
 <ul class="org-ul">
 <li>Gr (4.13)</li>
 </ul>
@@ -1749,7 +1749,7 @@ These <b>bound charges</b> faithfully represent the object's sources for electri
 </p>
 
 
-<div class="example div" id="orga521891">
+<div class="example div" id="orge4443d6">
 <p>
 <b>Example: uniformly polarized sphere</b>
 </p>
@@ -1827,7 +1827,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_po_fid.html b/build/emsm_esm_po_fid.html
index 52bc5bd..b65316f 100644
--- a/build/emsm_esm_po_fid.html
+++ b/build/emsm_esm_po_fid.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,14 +1638,14 @@ Therefore, \({\bf E}_{out}\) is the field at \({\bf r}\)
 from dipoles exterior to the sphere, for which we can use <a href="./emsm_esm_po.html#p_P">p_P</a>:
 </p>
 
-<div class="eqlabel" id="orgd0b898b">
+<div class="eqlabel" id="org84582b1">
 <p>
 <a id="p_out"></a><a href="./emsm_esm_po_fid.html#p_out"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgb11243d">
+<div class="alteqlabels" id="org3cb06f1">
 <ul class="org-ul">
 <li>Gr (4.17)</li>
 </ul>
@@ -1663,14 +1663,14 @@ The dipoles inside the sphere however cannot be treated in this fashion.
 However, their average field is all we need, and
 this is given by (see Example below for the derivation)
 </p>
-<div class="eqlabel" id="orgfbeede1">
+<div class="eqlabel" id="orgf056cb1">
 <p>
 <a id="Eavg_p"></a><a href="./emsm_esm_po_fid.html#Eavg_p"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orge636edb">
+<div class="alteqlabels" id="orga82d339">
 <ul class="org-ul">
 <li>Gr (3.105)</li>
 </ul>
@@ -1686,7 +1686,7 @@ this is given by (see Example below for the derivation)
 irrespective of charge distribution within sphere.
 </p>
 
-<div class="example div" id="org662d9cb">
+<div class="example div" id="org0100591">
 <p>
 <b>Average field inside a sphere</b>
 </p>
@@ -1823,7 +1823,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_esm_po_pibc.html b/build/emsm_esm_po_pibc.html
index d791222..9f40fb2 100644
--- a/build/emsm_esm_po_pibc.html
+++ b/build/emsm_esm_po_pibc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1656,7 +1656,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm.html b/build/emsm_msm.html
index c5b8e0b..e49727b 100644
--- a/build/emsm_msm.html
+++ b/build/emsm_msm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1614,8 +1614,8 @@ Table of contents
 </svg></a><span class="headline-id">emsm.msm</span></h3>
 
 <div class="outline-text-3" id="text-emsm_msm">
-<details class="prereq" id="org0cc6ee8">
-<summary id="org869f211">
+<details class="prereq" id="orga1d9067">
+<summary id="org84454e7">
 Prerequisites
 </summary>
 <ul class="org-ul">
@@ -1624,8 +1624,8 @@ Prerequisites
 </ul>
 </details>
 
-<details class="objectives" id="org2f9a388">
-<summary id="org66eb2cc">
+<details class="objectives" id="orgbbd9807">
+<summary id="org13513e2">
 Objectives
 </summary>
 <ul class="org-ul">
@@ -1664,7 +1664,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_H.html b/build/emsm_msm_H.html
index 31c4785..ed62ef3 100644
--- a/build/emsm_msm_H.html
+++ b/build/emsm_msm_H.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_H_A.html b/build/emsm_msm_H_A.html
index 9697695..205088b 100644
--- a/build/emsm_msm_H_A.html
+++ b/build/emsm_msm_H_A.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1617,14 +1617,14 @@ Table of contents
 Nomenclature:  as in electric case, we have bound currents, and everything else, which we call the <b>free current</b>.
 Total current:
 </p>
-<div class="eqlabel" id="org2f67ed9">
+<div class="eqlabel" id="orgf612a79">
 <p>
 <a id="JbJf"></a><a href="./emsm_msm_H_A.html#JbJf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8bc9595">
+<div class="alteqlabels" id="orgd462050">
 <ul class="org-ul">
 <li>Gr (6.17)</li>
 </ul>
@@ -1644,15 +1644,15 @@ Ampère's law:
 \]
 so we can define
 </p>
-<div class="core div" id="org1215d01">
-<div class="eqlabel" id="orgd5d9468">
+<div class="core div" id="orgb005d3f">
+<div class="eqlabel" id="orge90374d">
 <p>
 <a id="HBM"></a><a href="./emsm_msm_H_A.html#HBM"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org9ba5a4d">
+<div class="alteqlabels" id="org7acbd07">
 <ul class="org-ul">
 <li>Gr (6.18)</li>
 </ul>
@@ -1671,15 +1671,15 @@ so we can define
 <p>
 and rewrite Ampère's law as
 </p>
-<div class="core div" id="org18518e4">
-<div class="eqlabel" id="orga0d403e">
+<div class="core div" id="org498380a">
+<div class="eqlabel" id="orgacd7c31">
 <p>
 <a id="curlHJf"></a><a href="./emsm_msm_H_A.html#curlHJf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgec3bba4">
+<div class="alteqlabels" id="org1a7220e">
 <ul class="org-ul">
 <li>Gr (6.19)</li>
 </ul>
@@ -1698,15 +1698,15 @@ and rewrite Ampère's law as
 <p>
 or in integral form,
 </p>
-<div class="core div" id="org288c4e9">
-<div class="eqlabel" id="orgccd63b9">
+<div class="core div" id="org77499d2">
+<div class="eqlabel" id="orgf374008">
 <p>
 <a id="intHdl"></a><a href="./emsm_msm_H_A.html#intHdl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org9025220">
+<div class="alteqlabels" id="org9cbba67">
 <ul class="org-ul">
 <li>Gr (6.20)</li>
 </ul>
@@ -1727,7 +1727,7 @@ or in integral form,
 rewrite Ampère's law in terms of free currents alone.  Bound currents come along for the ride.
 </p>
 
-<div class="example div" id="org2556e80">
+<div class="example div" id="orgec3bc1c">
 <p>
 <b>Example: copper rod</b>
 </p>
@@ -1746,14 +1746,14 @@ Bound currents antiparallel to \(I\) in bulk and parallel at surface.  All curre
 so \({\bf B}, {\bf M}, {\bf H}\) are circumferential.  Apply integral form of Ampère's law with
 radius \(s &lt; R\):  \(H (2\pi s) = I_{f_{enc}} = I \frac{\pi s^2}{\pi R^2}\) so
 </p>
-<div class="eqlabel" id="orga2d5f0f">
+<div class="eqlabel" id="org645df4c">
 <p>
 <a id="Hrod_in"></a><a href="./emsm_msm_H_A.html#Hrod_in"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org6c30162">
+<div class="alteqlabels" id="orgd07686f">
 <ul class="org-ul">
 <li>Gr (6.21)</li>
 </ul>
@@ -1768,14 +1768,14 @@ radius \(s &lt; R\):  \(H (2\pi s) = I_{f_{enc}} = I \frac{\pi s^2}{\pi R^2}\) s
 \]
 Outside,
 </p>
-<div class="eqlabel" id="org3469141">
+<div class="eqlabel" id="org01a6ad4">
 <p>
 <a id="Hrod_out"></a><a href="./emsm_msm_H_A.html#Hrod_out"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org617ce83">
+<div class="alteqlabels" id="org8d46f2c">
 <ul class="org-ul">
 <li>Gr (6.22)</li>
 </ul>
@@ -1801,14 +1801,14 @@ There, \({\bf M} = 0\) so \({\bf B} = \mu_0 {\bf H}\).
 Similarly to electric case:  cannot assume that \({\bf H}\) is like \({\bf B}\).
 \({\bf H}\) might have a divergence,
 </p>
-<div class="eqlabel" id="org9d34023">
+<div class="eqlabel" id="org75b7450">
 <p>
 <a id="divH"></a><a href="./emsm_msm_H_A.html#divH"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgd156a25">
+<div class="alteqlabels" id="org4360dd3">
 <ul class="org-ul">
 <li>Gr (6.23)</li>
 </ul>
@@ -1869,14 +1869,14 @@ W_{mag} = \int_{all~space} d\tau \frac{1}{2} {\bf H} \cdot {\bf B}
 <p>
 Can rewrite BCs in terms of \({\bf H}\):  from <a href="./emsm_msm_H_A.html#divH">divH</a>,
 </p>
-<div class="eqlabel" id="orge31639d">
+<div class="eqlabel" id="org0d19976">
 <p>
 <a id="HdiscM"></a><a href="./emsm_msm_H_A.html#HdiscM"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga7ad559">
+<div class="alteqlabels" id="org23f8b3d">
 <ul class="org-ul">
 <li>Gr (6.24)</li>
 </ul>
@@ -1891,14 +1891,14 @@ H^{\perp}_{above} - H^{\perp}_{below} = -(M^{\perp}_{above} - M^{\perp}_{below})
 <p>
 while <a href="./emsm_msm_H_A.html#curlHJf">curlHJf</a> gives
 </p>
-<div class="eqlabel" id="org8258597">
+<div class="eqlabel" id="orgb5a3e26">
 <p>
 <a id="Hdisc"></a><a href="./emsm_msm_H_A.html#Hdisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org086a72c">
+<div class="alteqlabels" id="org43a8e56">
 <ul class="org-ul">
 <li>Gr (6.25)</li>
 </ul>
@@ -1943,7 +1943,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_a.html b/build/emsm_msm_a.html
index 4b3c4b0..6bcb67c 100644
--- a/build/emsm_msm_a.html
+++ b/build/emsm_msm_a.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1680,7 +1680,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_fmo.html b/build/emsm_msm_fmo.html
index ce931a3..4270528 100644
--- a/build/emsm_msm_fmo.html
+++ b/build/emsm_msm_fmo.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_fmo_bc.html b/build/emsm_msm_fmo_bc.html
index 604cb85..ca5834a 100644
--- a/build/emsm_msm_fmo_bc.html
+++ b/build/emsm_msm_fmo_bc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1624,15 +1624,15 @@ For a single dipole:  refer to <a href="./ems_ms_vp_me.html#A_di">A_di</a> (vect
 For a chunk of material with local magnetization \({\bf M} ({\bf r})\),
 by the principle of superposition we thus have:
 </p>
-<div class="main div" id="org2949db0">
-<div class="eqlabel" id="org8ef6e18">
+<div class="main div" id="org9e68a48">
+<div class="eqlabel" id="org87b7053">
 <p>
 <a id="A_M"></a><a href="./emsm_msm_fmo_bc.html#A_M"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgc1360ca">
+<div class="alteqlabels" id="orgdb02106">
 <ul class="org-ul">
 <li>Gr (6.11)</li>
 </ul>
@@ -1688,15 +1688,15 @@ leads to
 <p>
 Reinterpretation:  first term: potential from volume current,
 </p>
-<div class="main div" id="org4073ff1">
-<div class="eqlabel" id="orgcc588cc">
+<div class="main div" id="org9ee85b1">
+<div class="eqlabel" id="orga6d1998">
 <p>
 <a id="JbcurlM"></a><a href="./emsm_msm_fmo_bc.html#JbcurlM"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org428f7f2">
+<div class="alteqlabels" id="org0581992">
 <ul class="org-ul">
 <li>Gr (6.13)</li>
 </ul>
@@ -1715,15 +1715,15 @@ Reinterpretation:  first term: potential from volume current,
 <p>
 second term:  potential from surface current,
 </p>
-<div class="main div" id="org23bdcca">
-<div class="eqlabel" id="orgfa9f958">
+<div class="main div" id="org6d2f837">
+<div class="eqlabel" id="org5b0da1e">
 <p>
 <a id="KbM"></a><a href="./emsm_msm_fmo_bc.html#KbM"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org5e854f1">
+<div class="alteqlabels" id="orgb79e920">
 <ul class="org-ul">
 <li>Gr (6.14)</li>
 </ul>
@@ -1742,7 +1742,7 @@ second term:  potential from surface current,
 <p>
 With these definitions,
 </p>
-<div class="main div" id="org28ad325">
+<div class="main div" id="org9fd0a25">
 \begin{equation}
 {\bf A} ({\bf r}) = \frac{\mu_0}{4\pi} \int_{\cal V} d\tau' \frac{{\bf J}_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
     + \frac{\mu_0}{4\pi} \oint_{\cal S} da' \frac{{\bf K}_b ({\bf r}')}{|{\bf r} - {\bf r}'|}
@@ -1775,7 +1775,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_fmo_fim.html b/build/emsm_msm_fmo_fim.html
index 9005b95..7499dc9 100644
--- a/build/emsm_msm_fmo_fim.html
+++ b/build/emsm_msm_fmo_fim.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1635,7 +1635,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_fmo_pibc.html b/build/emsm_msm_fmo_pibc.html
index 778363c..19f654e 100644
--- a/build/emsm_msm_fmo_pibc.html
+++ b/build/emsm_msm_fmo_pibc.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_lnlm.html b/build/emsm_msm_lnlm.html
index 6e84863..888694b 100644
--- a/build/emsm_msm_lnlm.html
+++ b/build/emsm_msm_lnlm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_lnlm_fm.html b/build/emsm_msm_lnlm_fm.html
index 3a09717..5403a68 100644
--- a/build/emsm_msm_lnlm_fm.html
+++ b/build/emsm_msm_lnlm_fm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1636,7 +1636,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_lnlm_sp.html b/build/emsm_msm_lnlm_sp.html
index 6b42dfd..8ccba7a 100644
--- a/build/emsm_msm_lnlm_sp.html
+++ b/build/emsm_msm_lnlm_sp.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1618,15 +1618,15 @@ In para/diamagnets:  when \({\bf B}\) is removed, \({\bf M}\) disappears.  For n
 fields, proportionality.  Custom (slightly different than for dielectrics):
 <b>magnetic susceptibility</b> \(\chi_m\) defined as
 </p>
-<div class="core div" id="org93a7b9d">
-<div class="eqlabel" id="orge26d08e">
+<div class="core div" id="org0325484">
+<div class="eqlabel" id="orgbe890e7">
 <p>
 <a id="chim"></a><a href="./emsm_msm_lnlm_sp.html#chim"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org1848ac6">
+<div class="alteqlabels" id="orgdcb34ad">
 <ul class="org-ul">
 <li>Gr (6.29)</li>
 </ul>
@@ -1646,14 +1646,14 @@ fields, proportionality.  Custom (slightly different than for dielectrics):
 (and <b>not</b> \({\bf M} = \frac{1}{\mu_0} \chi_m {\bf B}\) had the electrostatics parallel
 been followed historically).  Materials that obey this are called <i>linear media</i>.  Then,
 </p>
-<div class="eqlabel" id="org7b5932a">
+<div class="eqlabel" id="org60f94e9">
 <p>
 <a id="BHM"></a><a href="./emsm_msm_lnlm_sp.html#BHM"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org8cddbc7">
+<div class="alteqlabels" id="org4392940">
 <ul class="org-ul">
 <li>Gr (6.30)</li>
 </ul>
@@ -1668,14 +1668,14 @@ been followed historically).  Materials that obey this are called <i>linear medi
 \]
 and thus
 </p>
-<div class="eqlabel" id="org5774258">
+<div class="eqlabel" id="org8fc13a8">
 <p>
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org95fbc74">
+<div class="alteqlabels" id="org080f01f">
 <ul class="org-ul">
 <li>Gr (6.31)</li>
 </ul>
@@ -1700,14 +1700,14 @@ have nonzero divergence.
 <p>
 In linear medium:  bound volume current proportional to free current,
 </p>
-<div class="eqlabel" id="orgff08ab2">
+<div class="eqlabel" id="orgf7e9000">
 <p>
 <a id="JbchimJf"></a><a href="./emsm_msm_lnlm_sp.html#JbchimJf"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org560487f">
+<div class="alteqlabels" id="orgd46d20d">
 <ul class="org-ul">
 <li>Gr (6.33)</li>
 </ul>
@@ -1742,7 +1742,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_m.html b/build/emsm_msm_m.html
index fd8f721..9c52dcb 100644
--- a/build/emsm_msm_m.html
+++ b/build/emsm_msm_m.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_m_dpf.html b/build/emsm_msm_m_dpf.html
index ff3ecd2..5ef3412 100644
--- a/build/emsm_msm_m_dpf.html
+++ b/build/emsm_msm_m_dpf.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1624,9 +1624,9 @@ Table of contents
 </p>
 </div>
 
-<div id="outline-container-org169405c" class="outline-6">
-<h6 id="org169405c"><a href="#org169405c">Why is Ferromagnetism such an intriguing phenomenon?</a></h6>
-<div class="outline-text-6" id="text-org169405c">
+<div id="outline-container-orgbe55b01" class="outline-6">
+<h6 id="orgbe55b01"><a href="#orgbe55b01">Why is Ferromagnetism such an intriguing phenomenon?</a></h6>
+<div class="outline-text-6" id="text-orgbe55b01">
 <p>
 [in construction]
 </p>
@@ -1652,7 +1652,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/emsm_msm_m_fdi.html b/build/emsm_msm_m_fdi.html
index 44fcb3c..68abb9b 100644
--- a/build/emsm_msm_m_fdi.html
+++ b/build/emsm_msm_m_fdi.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,15 +1616,15 @@ Table of contents
 <p>
 Torque on magnetic dipole:
 </p>
-<div class="core div" id="orgbecae08">
-<div class="eqlabel" id="org86842e9">
+<div class="core div" id="org862863d">
+<div class="eqlabel" id="org2941465">
 <p>
 <a id="NmB"></a><a href="./emsm_msm_m_fdi.html#NmB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org9fae006">
+<div class="alteqlabels" id="org92b73de">
 <ul class="org-ul">
 <li>Gr (6.1)</li>
 </ul>
@@ -1649,15 +1649,15 @@ Similar to electric analogue, <a href="./emsm_esm_mE_o.html#di_N">di_N</a>, \({\
 <p>
 In a non-uniform field:
 </p>
-<div class="main div" id="orgf91bfde">
-<div class="eqlabel" id="orgcba6a69">
+<div class="main div" id="orge40d4e5">
+<div class="eqlabel" id="orgd7e7808">
 <p>
 <a id="FgradmB"></a><a href="./emsm_msm_m_fdi.html#FgradmB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org2c23a3b">
+<div class="alteqlabels" id="orgbd81d81">
 <ul class="org-ul">
 <li>Gr (6.3)</li>
 </ul>
@@ -1693,7 +1693,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/fig/red/red_motion_under_cst_F.asy b/build/fig/red/red_motion_under_cst_F.asy
index 1bea700..e266d79 100644
--- a/build/fig/red/red_motion_under_cst_F.asy
+++ b/build/fig/red/red_motion_under_cst_F.asy
@@ -22,7 +22,7 @@ path cla = graph(Fcla, 0, 2);
 draw(cla, arrow=Arrow(), p=dashed+blue, L=Label(rotate(32)*"classical", position=MidPoint, align=2E));
 
 arrowbar axisarrow = Arrow(TeXHead);
-Label xlabel = Label("$t$", position=EndPoint);
+Label xlabel = Label("$x(t)$", position=EndPoint);
 draw((xmin, 0) -- (xmax, 0), arrow=axisarrow, L=xlabel);
-Label ylabel = Label("$x(t)$", position=EndPoint);
+Label ylabel = Label("$t$", position=EndPoint);
 draw((0, ymin) -- (0, ymax), arrow=axisarrow, L=ylabel);
diff --git a/build/fig/red/red_motion_under_cst_F.svg b/build/fig/red/red_motion_under_cst_F.svg
index d0112dc..4827e52 100644
--- a/build/fig/red/red_motion_under_cst_F.svg
+++ b/build/fig/red/red_motion_under_cst_F.svg
@@ -1,6 +1,6 @@
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diff --git a/build/in.html b/build/in.html
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+++ b/build/in.html
@@ -1,7 +1,7 @@
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-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
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@@ -1293,7 +1293,7 @@ Table of contents
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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diff --git a/build/in_p.html b/build/in_p.html
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@@ -1293,7 +1293,7 @@ Table of contents
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 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
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diff --git a/build/in_t.html b/build/in_t.html
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+<!-- 2022-03-24 Thu 08:42 -->
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@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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@@ -1638,7 +1638,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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diff --git a/build/in_t_c.html b/build/in_t_c.html
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@@ -1,7 +1,7 @@
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+<!-- 2022-03-24 Thu 08:42 -->
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@@ -1293,7 +1293,7 @@ Table of contents
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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@@ -1618,8 +1618,8 @@ Throughout these lecture notes, boxes with contextual colors are used,
 serving specific purposes. These are:
 </p>
 
-<details class="prereq" id="orgcd04899">
-<summary id="orgdb0c3c0">
+<details class="prereq" id="org5ffb4e1">
+<summary id="org04f58fb">
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 <p>
@@ -1632,8 +1632,8 @@ Specific prerequisites for understanding the upcoming material
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-<summary id="org7569856">
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 <p>
@@ -1646,8 +1646,8 @@ Objectives for this part: what you should learn by reading this
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 Main
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-<details class="example" id="org8ce185f">
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 Example
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-<details class="info" id="orgdecff2e">
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+<summary id="orgff3af00">
 Info
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-<summary id="org42a56ce">
+<details class="context" id="orgb816b1e">
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 Historical Context
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@@ -1709,7 +1709,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
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@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1673,7 +1673,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/index.html b/build/index.html
index 8567ba5..ee9a1bd 100644
--- a/build/index.html
+++ b/build/index.html
@@ -1,7 +1,7 @@
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 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1958,7 +1958,7 @@ Table of contents
 <li>
 <a href="./qed.html#qed">Quantum Electrodynamics</a><span class="headline-id">qed</span>
 <ul>
-<li><a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span></li>
+<li><a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span></li>
 </ul>
 </li>
 <li>
@@ -2091,7 +2091,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/qed.html b/build/qed.html
index 2643c3d..125fd2c 100644
--- a/build/qed.html
+++ b/build/qed.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1607,7 +1607,7 @@ Table of contents
 </ul>
 </details>
 </nav>
-<ul class="breadcrumbs"><li>Quantum Electrodynamics</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="qed_t.html">QED today&emsp;<small>[qed.t]</small></a></li></ul>
+<ul class="breadcrumbs"><li>Quantum Electrodynamics</li></ul><ul class="navigation-links"><li>Next:&nbsp;<a href="qed_L.html">Lagrangian&emsp;<small>[qed.L]</small></a></li></ul>
 <h2 id="qed">Quantum Electrodynamics<a class="headline-permalink" href="./qed.html#qed"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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@@ -1619,10 +1619,10 @@ Table of contents
 
 <h3>In this section:</h3>
 <ul class="child-links-list">
-<li><a href="qed_t.html">QED today</a><span class="headline-id">qed.t</span></li>
+<li><a href="qed_L.html">Lagrangian</a><span class="headline-id">qed.L</span></li>
 </ul>
 
-<br><ul class="navigation-links"><li>Next:&nbsp;<a href="qed_t.html">QED today&emsp;<small>[qed.t]</small></a></li></ul>
+<br><ul class="navigation-links"><li>Next:&nbsp;<a href="qed_L.html">Lagrangian&emsp;<small>[qed.L]</small></a></li></ul>
 <br>
 <hr>
 <div class="license">
@@ -1637,7 +1637,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
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deleted file mode 100644
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-Table of contents
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-<ul>
-<li>
-
-<details>
-<summary>
-<a href="./in.html#in">Introduction</a><span class="headline-id">in</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./in_p.html#in_p">Preface</a><span class="headline-id">in.p</span>
-
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./in_t.html#in_t">Tips for the reader</a><span class="headline-id">in.t</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./in_t_l.html#in_t_l">Section and equation labelling</a><span class="headline-id">in.t.l</span>
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-</li>
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-<a href="./in_t_c.html#in_t_c">Contextual colors</a><span class="headline-id">in.t.c</span>
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-</li>
-
-</ul>
-</details>
-</li>
-
-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./ems.html#ems">Electromagnetostatics</a><span class="headline-id">ems</span>
-
-
-</summary>
-<ul>
-<li>
-
-<details>
-<summary>
-<a href="./ems_es.html#ems_es">Electrostatics</a><span class="headline-id">ems.es</span>
-
-
-</summary>
-<ul>
-<li>
-
-<details>
-<summary>
-<a href="./ems_es_ec.html#ems_es_ec">Electric Charge</a><span class="headline-id">ems.es.ec</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./ems_es_ec_b.html#ems_es_ec_b">Basics</a><span class="headline-id">ems.es.ec.b</span>
-
-</li>
-<li>
-<a href="./ems_es_ec_c.html#ems_es_ec_c">Conservation</a><span class="headline-id">ems.es.ec.c</span>
-
-</li>
-<li>
-<a href="./ems_es_ec_q.html#ems_es_ec_q">Quantization</a><span class="headline-id">ems.es.ec.q</span>
-
-</li>
-<li>
-<a href="./ems_es_ec_s.html#ems_es_ec_s">Structure</a><span class="headline-id">ems.es.ec.s</span>
-
-</li>
-
-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./ems_es_efo.html#ems_es_efo">Electric Force and Energy</a><span class="headline-id">ems.es.efo</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./ems_es_efo_cl.html#ems_es_efo_cl">Coulomb's Law</a><span class="headline-id">ems.es.efo.cl</span>
-
-</li>
-<li>
-<a href="./ems_es_efo_ps.html#ems_es_efo_ps">Principle of Superposition</a><span class="headline-id">ems.es.efo.ps</span>
-
-</li>
-<li>
-<a href="./ems_es_efo_exp.html#ems_es_efo_exp">Experimental Investigations</a><span class="headline-id">ems.es.efo.exp</span>
-
-</li>
-<li>
-<a href="./ems_es_efo_e.html#ems_es_efo_e">Energy in Systems of Point Charges</a><span class="headline-id">ems.es.efo.e</span>
-
-</li>
-
-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./ems_es_ef.html#ems_es_ef">Electrostatic Fields</a><span class="headline-id">ems.es.ef</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./ems_es_ef_pc.html#ems_es_ef_pc">Electrostatic Field of Point Charges</a><span class="headline-id">ems.es.ef.pc</span>
-
-</li>
-<li>
-<a href="./ems_es_ef_ccd.html#ems_es_ef_ccd">Electrostatic Field of Continuous Charge Distributions</a><span class="headline-id">ems.es.ef.ccd</span>
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-</li>
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-</li>
-
-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./ems_es_ep.html#ems_es_ep">The Electrostatic Potential</a><span class="headline-id">ems.es.ep</span>
-
-
-</summary>
-<ul>
-<li>
-<a href="./ems_es_ep_d.html#ems_es_ep_d">Definition</a><span class="headline-id">ems.es.ep.d</span>
-
-</li>
-<li>
-<a href="./ems_es_ep_fp.html#ems_es_ep_fp">Field in terms of the potential</a><span class="headline-id">ems.es.ep.fp</span>
-
-</li>
-<li>
-<a href="./ems_es_ep_ex.html#ems_es_ep_ex">Example calculations for the potential</a><span class="headline-id">ems.es.ep.ex</span>
-
-</li>
-<li>
-<a href="./ems_es_ep_PL.html#ems_es_ep_PL">Poisson's and Laplace's Equations</a><span class="headline-id">ems.es.ep.PL</span>
-
-</li>
-<li>
-<a href="./ems_es_ep_bc.html#ems_es_ep_bc">Electrostatic Boundary Conditions</a><span class="headline-id">ems.es.ep.bc</span>
-
-</li>
-
-</ul>
-</details>
-</li>
-<li>
-<a href="./ems_es_e.html#ems_es_e">Electrostatic Energy from the Potential</a><span class="headline-id">ems.es.e</span>
-
-</li>
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-
-<details>
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-<a href="./ems_es_c.html#ems_es_c">Conductors</a><span class="headline-id">ems.es.c</span>
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-
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-<ul>
-<li>
-<a href="./ems_es_c_p.html#ems_es_c_p">Properties</a><span class="headline-id">ems.es.c.p</span>
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-</li>
-<li>
-<a href="./ems_es_c_ic.html#ems_es_c_ic">Induced Charges</a><span class="headline-id">ems.es.c.ic</span>
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-</li>
-<li>
-<a href="./ems_es_c_sc.html#ems_es_c_sc">Surface Charge and the Force on a Conductor</a><span class="headline-id">ems.es.c.sc</span>
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-</li>
-<li>
-<a href="./ems_es_c_cap.html#ems_es_c_cap">Capacitors</a><span class="headline-id">ems.es.c.cap</span>
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-</ul>
-</details>
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-</ul>
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-<summary>
-<a href="./ems_ca.html#ems_ca">Calculating or Approximating the Electrostatic Potential</a><span class="headline-id">ems.ca</span>
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-</summary>
-<ul>
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-<summary>
-<a href="./ems_ca_fe.html#ems_ca_fe">Fundamental Equations for the Electrostatic Potential</a><span class="headline-id">ems.ca.fe</span>
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-</summary>
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-<li>
-<a href="./ems_ca_fe_L.html#ems_ca_fe_L">The Laplace Equation</a><span class="headline-id">ems.ca.fe.L</span>
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-<li>
-<a href="./ems_ca_fe_g.html#ems_ca_fe_g">Green's Identities</a><span class="headline-id">ems.ca.fe.g</span>
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-</li>
-<li>
-<a href="./ems_ca_fe_uP.html#ems_ca_fe_uP">Uniqueness of Solution to Poisson's Equation</a><span class="headline-id">ems.ca.fe.uP</span>
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-</li>
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-</ul>
-</details>
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-<li>
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-<details>
-<summary>
-<a href="./ems_ca_mi.html#ems_ca_mi">The Method of Images</a><span class="headline-id">ems.ca.mi</span>
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-</summary>
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-<li>
-<a href="./ems_ca_mi_isc.html#ems_ca_mi_isc">Induced Surface Charges</a><span class="headline-id">ems.ca.mi.isc</span>
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-<a href="./ems_ca_mi_fe.html#ems_ca_mi_fe">Force and Energy</a><span class="headline-id">ems.ca.mi.fe</span>
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-<li>
-<a href="./ems_ca_mi_o.html#ems_ca_mi_o">Other Image Problems</a><span class="headline-id">ems.ca.mi.o</span>
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-</li>
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-</ul>
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-<summary>
-<a href="./ems_ca_sv.html#ems_ca_sv">Separation of Variables</a><span class="headline-id">ems.ca.sv</span>
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-</summary>
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-<a href="./ems_ca_sv_car.html#ems_ca_sv_car">Cartesian Coordinates</a><span class="headline-id">ems.ca.sv.car</span>
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-<li>
-<a href="./ems_ca_sv_cyl.html#ems_ca_sv_cyl">Cylindrical Coordinates</a><span class="headline-id">ems.ca.sv.cyl</span>
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-<li>
-<a href="./ems_ca_sv_sph.html#ems_ca_sv_sph">Spherical Coordinates</a><span class="headline-id">ems.ca.sv.sph</span>
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-</li>
-
-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./ems_ca_me.html#ems_ca_me">The Multipole Expansion</a><span class="headline-id">ems.ca.me</span>
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-</summary>
-<ul>
-<li>
-<a href="./ems_ca_me_a.html#ems_ca_me_a">Approximate Potential at Large Distance</a><span class="headline-id">ems.ca.me.a</span>
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-<li>
-<a href="./ems_ca_me_md.html#ems_ca_me_md">Monopole and Dipole Terms</a><span class="headline-id">ems.ca.me.md</span>
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-<li>
-<a href="./ems_ca_me_h.html#ems_ca_me_h">Higher Moments</a><span class="headline-id">ems.ca.me.h</span>
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-</li>
-<li>
-<a href="./ems_ca_me_Ed.html#ems_ca_me_Ed">The Electric Field of a Dipole</a><span class="headline-id">ems.ca.me.Ed</span>
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-</li>
-<li>
-<a href="./ems_ca_me_Eq.html#ems_ca_me_Eq">The Electric Field of a Quadrupole</a><span class="headline-id">ems.ca.me.Eq</span>
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-</li>
-
-</ul>
-</details>
-</li>
-
-</ul>
-</details>
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-<li>
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-<details>
-<summary>
-<a href="./ems_ms.html#ems_ms">Magnetostatics</a><span class="headline-id">ems.ms</span>
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-</summary>
-<ul>
-<li>
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-<a href="./ems_ms_lf.html#ems_ms_lf">Charges in Motion: the Lorentz Force Law</a><span class="headline-id">ems.ms.lf</span>
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-</summary>
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-<a href="./ems_ms_lf_pc.html#ems_ms_lf_pc">Point Charges</a><span class="headline-id">ems.ms.lf.pc</span>
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-<li>
-<a href="./ems_ms_lf_sc.html#ems_ms_lf_sc">Steady Currents</a><span class="headline-id">ems.ms.lf.sc</span>
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-</ul>
-</details>
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-<li>
-<a href="./ems_ms_ce.html#ems_ms_ce">Charge Conservation and the Continuity Equation</a><span class="headline-id">ems.ms.ce</span>
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-<li>
-<a href="./ems_ms_BS.html#ems_ms_BS">Steady Currents: the Biot-Savart Law</a><span class="headline-id">ems.ms.BS</span>
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-<a href="./ems_ms_dcB.html#ems_ms_dcB">Divergence and Curl of \({\bf B}\)</a><span class="headline-id">ems.ms.dcB</span>
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-</summary>
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-<a href="./ems_ms_dcB_iw.html#ems_ms_dcB_iw">Simplistic case: infinite wire</a><span class="headline-id">ems.ms.dcB.iw</span>
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-<a href="./ems_ms_dcB_d.html#ems_ms_dcB_d">Divergence of \({\bf B}\) from Biot-Savart</a><span class="headline-id">ems.ms.dcB.d</span>
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-<a href="./ems_ms_dcB_c.html#ems_ms_dcB_c">Curl of \({\bf B}\) from Biot-Savart; Ampère's Law</a><span class="headline-id">ems.ms.dcB.c</span>
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-</ul>
-</details>
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-<li>
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-<summary>
-<a href="./ems_ms_vp.html#ems_ms_vp">The Vector Potential</a><span class="headline-id">ems.ms.vp</span>
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-<li>
-<a href="./ems_ms_vp_A.html#ems_ms_vp_A">Definition; Gauge Choices</a><span class="headline-id">ems.ms.vp.A</span>
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-</li>
-<li>
-<a href="./ems_ms_vp_mbc.html#ems_ms_vp_mbc">Magnetic Boundary Conditions</a><span class="headline-id">ems.ms.vp.mbc</span>
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-<li>
-<a href="./ems_ms_vp_me.html#ems_ms_vp_me">Multipole Expansion of the Vector Potential</a><span class="headline-id">ems.ms.vp.me</span>
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-</li>
-<li>
-<a href="./ems_ms_vp_comp.html#ems_ms_vp_comp">Comparison of Electrostatics and Magnetostatics</a><span class="headline-id">ems.ms.vp.comp</span>
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-<li>
-<a href="./ems_ms_vp_LC.html#ems_ms_vp_LC">The Levi-Civita Symbol</a><span class="headline-id">ems.ms.vp.LC</span>
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-</ul>
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-</ul>
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-<summary>
-<a href="./emsm.html#emsm">Electromagnetostatics in matter</a><span class="headline-id">emsm</span>
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-<ul>
-<li>
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-<summary>
-<a href="./emsm_esm.html#emsm_esm">Electrostatics in matter</a><span class="headline-id">emsm.esm</span>
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-<li>
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-<summary>
-<a href="./emsm_esm_mE.html#emsm_esm_mE">Matter Bathed in E Fields; Polarization</a><span class="headline-id">emsm.esm.mE</span>
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-<a href="./emsm_esm_mE_o.html#emsm_esm_mE_o">Overview</a><span class="headline-id">emsm.esm.mE.o</span>
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-<li>
-<a href="./emsm_esm_mE_P.html#emsm_esm_mE_P">Polarization</a><span class="headline-id">emsm.esm.mE.P</span>
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-<a href="./emsm_esm_po.html#emsm_esm_po">Polarized Objects; Bound Charges</a><span class="headline-id">emsm.esm.po</span>
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-<a href="./emsm_esm_po_pibc.html#emsm_esm_po_pibc">Physical Interpretation of Bound Charges</a><span class="headline-id">emsm.esm.po.pibc</span>
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-</li>
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-<a href="./emsm_esm_po_fid.html#emsm_esm_po_fid">The Field Inside a Dielectric</a><span class="headline-id">emsm.esm.po.fid</span>
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-<li>
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-<summary>
-<a href="./emsm_esm_D.html#emsm_esm_D">The Electric Displacement</a><span class="headline-id">emsm.esm.D</span>
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-<a href="./emsm_esm_D_bc.html#emsm_esm_D_bc">Boundary Conditions</a><span class="headline-id">emsm.esm.D.bc</span>
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-</details>
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-<li>
-<a href="./emsm_esm_di.html#emsm_esm_di">Dielectrics</a><span class="headline-id">emsm.esm.di</span>
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-<a href="./emsm_esm_ld.html#emsm_esm_ld">Linear Dielectrics</a><span class="headline-id">emsm.esm.ld</span>
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-<a href="./emsm_esm_ld_sp.html#emsm_esm_ld_sp">Susceptibility, Permittivity, Dielectric Constant</a><span class="headline-id">emsm.esm.ld.sp</span>
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-<a href="./emsm_esm_ld_bvp.html#emsm_esm_ld_bvp">Boundary Value Problems with Linear Dielectrics</a><span class="headline-id">emsm.esm.ld.bvp</span>
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-<a href="./emsm_esm_ld_e.html#emsm_esm_ld_e">Energy in Dielectric Systems</a><span class="headline-id">emsm.esm.ld.e</span>
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-<a href="./emsm_esm_ld_f.html#emsm_esm_ld_f">Forces on Dielectrics</a><span class="headline-id">emsm.esm.ld.f</span>
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-</ul>
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-<a href="./emsm_msm.html#emsm_msm">Magnetostatics in matter</a><span class="headline-id">emsm.msm</span>
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-</summary>
-<ul>
-<li>
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-<summary>
-<a href="./emsm_msm_m.html#emsm_msm_m">Magnetization</a><span class="headline-id">emsm.msm.m</span>
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-</summary>
-<ul>
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-<a href="./emsm_msm_m_dpf.html#emsm_msm_m_dpf">Diamagnetism, Paramagnetism, Ferromagnetism</a><span class="headline-id">emsm.msm.m.dpf</span>
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-<a href="./emsm_msm_m_fdi.html#emsm_msm_m_fdi">Torques and Forces on Magnetic Dipoles</a><span class="headline-id">emsm.msm.m.fdi</span>
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-<a href="./emsm_msm_a.html#emsm_msm_a">Effect of Magnetic Field on Atomic Orbits</a><span class="headline-id">emsm.msm.a</span>
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-</li>
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-</details>
-</li>
-<li>
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-<summary>
-<a href="./emsm_msm_fmo.html#emsm_msm_fmo">The Field of a Magnetized Object</a><span class="headline-id">emsm.msm.fmo</span>
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-<li>
-<a href="./emsm_msm_fmo_bc.html#emsm_msm_fmo_bc">Bound Currents</a><span class="headline-id">emsm.msm.fmo.bc</span>
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-<li>
-<a href="./emsm_msm_fmo_pibc.html#emsm_msm_fmo_pibc">Physical Interpretation of Bound Currents</a><span class="headline-id">emsm.msm.fmo.pibc</span>
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-</li>
-<li>
-<a href="./emsm_msm_fmo_fim.html#emsm_msm_fmo_fim">The Magnetic Field Inside Matter</a><span class="headline-id">emsm.msm.fmo.fim</span>
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-</li>
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-</details>
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-<li>
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-<summary>
-<a href="./emsm_msm_H.html#emsm_msm_H">The H Field</a><span class="headline-id">emsm.msm.H</span>
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-<a href="./emsm_msm_H_A.html#emsm_msm_H_A">Ampère's Law in Magnetized Materials</a><span class="headline-id">emsm.msm.H.A</span>
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-</li>
-<li>
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-<summary>
-<a href="./emsm_msm_lnlm.html#emsm_msm_lnlm">Linear and Nonlinear Media</a><span class="headline-id">emsm.msm.lnlm</span>
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-</summary>
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-<a href="./emsm_msm_lnlm_sp.html#emsm_msm_lnlm_sp">Magnetic Susceptibility and Permeability</a><span class="headline-id">emsm.msm.lnlm.sp</span>
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-<a href="./emsm_msm_lnlm_fm.html#emsm_msm_lnlm_fm">Ferromagnetism</a><span class="headline-id">emsm.msm.lnlm.fm</span>
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-</ul>
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-</ul>
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-<details>
-<summary>
-<a href="./emd.html#emd">Electromagnetodynamics</a><span class="headline-id">emd</span>
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-</summary>
-<ul>
-<li>
-
-<details>
-<summary>
-<a href="./emd_Fl.html#emd_Fl">Induction: Faraday's Law</a><span class="headline-id">emd.Fl</span>
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-</summary>
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-<li>
-<a href="./emd_Fl_Fl.html#emd_Fl_Fl">Faraday's Law</a><span class="headline-id">emd.Fl.Fl</span>
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-<li>
-<a href="./emd_Fl_ief.html#emd_Fl_ief">The Induced Electric Field</a><span class="headline-id">emd.Fl.ief</span>
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-</li>
-<li>
-<a href="./emd_Fl_i.html#emd_Fl_i">Inductance</a><span class="headline-id">emd.Fl.i</span>
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-<li>
-<a href="./emd_Fl_e.html#emd_Fl_e">Energy in Magnetic Fields</a><span class="headline-id">emd.Fl.e</span>
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-</ul>
-</details>
-</li>
-<li>
-
-<details>
-<summary>
-<a href="./emd_Me.html#emd_Me">Maxwell's Equations</a><span class="headline-id">emd.Me</span>
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-</summary>
-<ul>
-<li>
-<a href="./emd_Me_ebM.html#emd_Me_ebM">Electrodynamics Before Maxwell</a><span class="headline-id">emd.Me.ebM</span>
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-<li>
-<a href="./emd_Me_dc.html#emd_Me_dc">Maxwell's Correction to Ampère's Law; the Displacement Current</a><span class="headline-id">emd.Me.dc</span>
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-</li>
-<li>
-<a href="./emd_Me_Me.html#emd_Me_Me">Maxwell's Equations</a><span class="headline-id">emd.Me.Me</span>
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-<li>
-<a href="./emd_Me_mc.html#emd_Me_mc">Magnetic Charge</a><span class="headline-id">emd.Me.mc</span>
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-</ul>
-</details>
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-<li>
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-<details>
-<summary>
-<a href="./emd_ce.html#emd_ce">Charge and Energy Flows</a><span class="headline-id">emd.ce</span>
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-</summary>
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-<li>
-<a href="./emd_ce_ce.html#emd_ce_ce">The Continuity Equation</a><span class="headline-id">emd.ce.ce</span>
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-</li>
-<li>
-<a href="./emd_ce_poy.html#emd_ce_poy">Poynting's Theorem; the Poynting Vector</a><span class="headline-id">emd.ce.poy</span>
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-</li>
-<li>
-<a href="./emd_ce_mst.html#emd_ce_mst">Maxwell's Stress Tensor</a><span class="headline-id">emd.ce.mst</span>
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-<li>
-<a href="./emd_ce_mom.html#emd_ce_mom">Momentum</a><span class="headline-id">emd.ce.mom</span>
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-<li>
-<a href="./emd_ce_amom.html#emd_ce_amom">Angular Momentum</a><span class="headline-id">emd.ce.amom</span>
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-</ul>
-</details>
-</li>
-<li>
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-<details>
-<summary>
-<a href="./emd_emw.html#emd_emw">Electromagnetic waves in vacuum</a><span class="headline-id">emd.emw</span>
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-</summary>
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-<li>
-<a href="./emd_emw_we.html#emd_emw_we">The Wave Equation</a><span class="headline-id">emd.emw.we</span>
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-<li>
-<a href="./emd_emw_mpw.html#emd_emw_mpw">Monochromatic Plane Waves</a><span class="headline-id">emd.emw.mpw</span>
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-<li>
-<a href="./emd_emw_ep.html#emd_emw_ep">Energy and Momentum</a><span class="headline-id">emd.emw.ep</span>
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-</details>
-</li>
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-</ul>
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-<summary>
-<a href="./emdm.html#emdm">Electromagnetodynamics in Matter</a><span class="headline-id">emdm</span>
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-<ul>
-<li>
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-<details>
-<summary>
-<a href="./emdm_Me.html#emdm_Me">Maxwell's Equations in Matter</a><span class="headline-id">emdm.Me</span>
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-<li>
-<a href="./emdm_Me_Mem.html#emdm_Me_Mem">Maxwell's Equations in Matter</a><span class="headline-id">emdm.Me.Mem</span>
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-<li>
-<a href="./emdm_Me_bc.html#emdm_Me_bc">Boundary Conditions</a><span class="headline-id">emdm.Me.bc</span>
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-</ul>
-</details>
-</li>
-<li>
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-<details>
-<summary>
-<a href="./emdm_emwm.html#emdm_emwm">Electromagnetic Waves in Matter</a><span class="headline-id">emdm.emwm</span>
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-<li>
-<a href="./emdm_emwm_plm.html#emdm_emwm_plm">Propagation in Linear Media</a><span class="headline-id">emdm.emwm.plm</span>
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-<a href="./emdm_emwm_refr.html#emdm_emwm_refr">Refraction</a><span class="headline-id">emdm.emwm.refr</span>
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-<summary>
-<a href="./emdm_emwm_refl.html#emdm_emwm_refl">Reflection and Transmission</a><span class="headline-id">emdm.emwm.refl</span>
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-<a href="./emdm_emwm_refl_ni.html#emdm_emwm_refl_ni">Normal Incidence</a><span class="headline-id">emdm.emwm.refl.ni</span>
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-<a href="./emdm_emwm_refl_oi.html#emdm_emwm_refl_oi">Oblique Incidence</a><span class="headline-id">emdm.emwm.refl.oi</span>
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-</li>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
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+<details class="prereq" id="org316cbb2">
+<summary id="org33dd1ea">
 Prerequisites
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 <ul class="org-ul">
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-<summary id="org4ca34fc">
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+<summary id="org2676b5b">
 Objectives
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@@ -1667,7 +1667,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
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 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1640,7 +1640,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
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 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1622,12 +1622,16 @@ in which \(\Lambda\) is a matrix representing the Lorentz transformation.
 The form this matrix takes depends on the actual transformation: for the specific
 case of motion in the \(x\) direction with velocity \(v\),
 \[
-  \Lambda = \left( \begin{array}{cccc}
+  \Lambda^\mu{}_\nu = \left( \begin{array}{cccc}
     \gamma &amp; -\gamma \beta &amp; 0 &amp; 0 \\
     -\gamma \beta &amp; \gamma &amp; 0 &amp; 0 \\
     0 &amp; 0 &amp; 1 &amp; 0 \\
-    0 &amp; 0 &amp; 0 &amp; 1 \end{array} \right).
+    0 &amp; 0 &amp; 0 &amp; 1 \end{array} \right)
 \]
+(in which \(\mu\) is the "row" index and \(\nu\) the "column" one).
+</p>
+
+<p>
 A four-vector is synonymous to a <b>rank-one tensor</b>.
 Higher-rank tensors are simply objects carrying more indices.
 For example, a <b>rank-two tensor</b> transforms as
@@ -1683,18 +1687,18 @@ how the nonvanishing elements of an antisymmetric tensor transform:
 <p>
 Comparing with the transformation rules for the electromagnetic field which we obtained in <a href="./red_rem_Ltf.html#EMtr">EMtr</a>, we can define the
 </p>
-<div class="core div" id="org117de8f">
+<div class="core div" id="orgf4b9c4f">
 <p>
 <b>Electromagnetic Field Tensor</b>
 </p>
-<div class="eqlabel" id="org358ea94">
+<div class="eqlabel" id="org81eea70">
 <p>
 <a id="Fmunu"></a><a href="./red_rem_Fmunu.html#Fmunu"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org597a4d9">
+<div class="alteqlabels" id="org185605b">
 
 </div>
 
@@ -1714,18 +1718,18 @@ F^{\mu \nu} = \left( \begin{array}{cccc}
 <p>
 together with the handy
 </p>
-<div class="main div" id="orgc56f47d">
+<div class="main div" id="orgc181a2e">
 <p>
 <b>Dual Field Tensor</b>
 </p>
-<div class="eqlabel" id="orgda1a353">
+<div class="eqlabel" id="orgc4536aa">
 <p>
 <a id="Gmunu"></a><a href="./red_rem_Fmunu.html#Gmunu"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org31f1240">
+<div class="alteqlabels" id="orgbf03668">
 
 </div>
 
@@ -1753,18 +1757,18 @@ obtained from the field tensor by the substitution
 <p>
 Our electromagnetic field transformation laws then become the simple
 </p>
-<div class="core div" id="org0e51dab">
+<div class="core div" id="org0260e5e">
 <p>
 <b>Lorentz Transformation Rules for EM Fields</b>
 </p>
-<div class="eqlabel" id="org41f872c">
+<div class="eqlabel" id="org75fce95">
 <p>
 <a id="LorF"></a><a href="./red_rem_Fmunu.html#LorF"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgbfcae60">
+<div class="alteqlabels" id="org854087d">
 
 </div>
 
@@ -1798,7 +1802,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rem_Ltf.html b/build/red_rem_Ltf.html
index 9fab40f..9957b50 100644
--- a/build/red_rem_Ltf.html
+++ b/build/red_rem_Ltf.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1615,7 +1615,7 @@ Table of contents
 <div class="outline-text-4" id="text-red_rem_Ltf">
 <p>
 Now that we know that what one observer sees as an electric field
-can be view by another as a magnetic field, we can ask the general
+can be viewed by another as a magnetic field, we can ask the general
 question of how fields transform upon Lorentz transformations.
 </p>
 
@@ -1674,7 +1674,7 @@ This magnetic field between the plates is thus
 
 <p>
 If we now have a further referential frame \(\bar{S}\) moving at velocity
-\(\bar{v}\) with respect to the original one, we'd have
+\(v\) with respect to \({\cal S}\) (and \(\bar{v}\) with respect to the original one), we'd have
 \[
   \bar{E}_y = \frac{\bar{\sigma}}{\varepsilon_0}, \hspace{10mm}
   \bar{B}_z = - \mu_0 \bar{\sigma} \bar{v}
@@ -1682,8 +1682,8 @@ If we now have a further referential frame \(\bar{S}\) moving at velocity
 where
 \[
   \bar{v} = \frac{v + v_0}{1 + v v_0/c^2}, \hspace{10mm}
-  \bar{\sigma} = \bar{\gamma} \sigma, \hspace{10mm}
-  \bar{\gamma} = \frac{1}{1 - \bar{v}^2/c^2}.
+  \bar{\sigma} = \bar{\gamma} \sigma_0, \hspace{10mm}
+  \bar{\gamma} = \frac{1}{\sqrt{1 - \bar{v}^2/c^2}}.
 \]
 </p>
 
@@ -1691,8 +1691,8 @@ where
 
 <p>
 We now want to express \(\bar{\boldsymbol E}, \bar{\boldsymbol B}\) in terms of
-\({\boldsymbol E}, {\boldsymbol B}\) and other data in frame \({\cal S}\)
-(here: \(v\)). To start, we have
+\({\boldsymbol E}, {\boldsymbol B}\) and other data in frame \({\cal S}\).
+To start, we have
 \[
   \bar{E}_y = \frac{\bar{\gamma}}{\gamma_0} \frac{\sigma}{\varepsilon_0},
   \hspace{10mm}
@@ -1736,28 +1736,28 @@ These factors cancel so \(\bar{B}_x = B_x\).
 <p>
 We thus obtain the
 </p>
-<div class="core div" id="orgf512c1f">
+<div class="core div" id="org3cf1e4c">
 <p>
 <b>EM field transformation laws</b> <i>(motion along \(x\) with velocity \(v\))</i>
 </p>
-<div class="eqlabel" id="org93bd238">
+<div class="eqlabel" id="orgc368b6d">
 <p>
 <a id="EMtr"></a><a href="./red_rem_Ltf.html#EMtr"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf5395d1">
+<div class="alteqlabels" id="orga9279ba">
 
 </div>
 
 </div>
 \begin{align}
   \bar{E}_x &amp;= E_x, \hspace{10mm} &amp;
-  \bar{E}_y &amp;= \gamma (E_y - v B_z), \hspace{10mm} &amp;
-  \bar{E}_z &amp;= \gamma (E_z + v B_y), \\
-  \bar{B}_x &amp;= B_x, &amp;
-  \bar{B}_y &amp;= \gamma \left( B_y + \frac{v}{c^2} E_z \right), &amp;
+  \bar{B}_x &amp;= B_x, \nonumber \\
+  \bar{E}_y &amp;= \gamma (E_y - v B_z), &amp;
+  \bar{B}_y &amp;= \gamma \left( B_y + \frac{v}{c^2} E_z \right), \nonumber \\
+  \bar{E}_z &amp;= \gamma (E_z + v B_y), &amp;
   \bar{B}_z &amp;= \gamma \left( B_z - \frac{v}{c^2} E_y \right)
   \tag{EMtr}\label{EMtr}
 \end{align}
@@ -1805,7 +1805,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rem_Me.html b/build/red_rem_Me.html
index 5b0096f..437aab9 100644
--- a/build/red_rem_Me.html
+++ b/build/red_rem_Me.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1637,18 +1637,18 @@ We thus obtain
 \]
 Recognizing the proper velocity, we thus get that charge density and current density can together form the
 </p>
-<div class="core div" id="org4a23d61">
+<div class="core div" id="orgf77fa2c">
 <p>
 <b>Current density 4-vector</b>
 </p>
-<div class="eqlabel" id="org8494a4a">
+<div class="eqlabel" id="orge15b585">
 <p>
 <a id="Jmu"></a><a href="./red_rem_Me.html#Jmu"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org63c21fa">
+<div class="alteqlabels" id="org284753c">
 
 </div>
 
@@ -1665,18 +1665,18 @@ J^\mu = \left( c\rho, J_x, J_y, J_z \right)
 <p>
 The continuity equation <a href="./ems_ms_ce.html#conteq">conteq</a> takes the simple form
 </p>
-<div class="core div" id="org2a3444b">
+<div class="core div" id="org10f61ee">
 <p>
 <b>Continuity equation</b>
 </p>
-<div class="eqlabel" id="org2db5045">
+<div class="eqlabel" id="orgb3448db">
 <p>
 <a id="conteq_rel"></a><a href="./red_rem_Me.html#conteq_rel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org830511b">
+<div class="alteqlabels" id="org24d637d">
 
 </div>
 
@@ -1692,18 +1692,18 @@ The continuity equation <a href="./ems_ms_ce.html#conteq">conteq</a> takes the s
 <p>
 while similarly the notation simplifies for
 </p>
-<div class="main div" id="org0816f0a">
+<div class="main div" id="org5eaabdd">
 <p>
 <b>Maxwell's equations</b>
 </p>
-<div class="eqlabel" id="org3cc1fa8">
+<div class="eqlabel" id="orgb5e9ffe">
 <p>
 <a id="Max_rel"></a><a href="./red_rem_Me.html#Max_rel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="org77d9519">
+<div class="alteqlabels" id="org5bacda7">
 
 </div>
 
@@ -1722,18 +1722,18 @@ while similarly the notation simplifies for
 <p>
 In terms of \(F^{\mu \nu}\) and the proper velocity \(\eta^\mu\), we also have the
 </p>
-<div class="main div" id="orge8ec801">
+<div class="main div" id="org2e4c192">
 <p>
 <b>Minkowski force on a charge</b> \(q\)
 </p>
-<div class="eqlabel" id="org467f39b">
+<div class="eqlabel" id="org48b2b5f">
 <p>
 <a id="MinkF_rel"></a><a href="./red_rem_Me.html#MinkF_rel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf90a88d">
+<div class="alteqlabels" id="org5e3e23a">
 
 </div>
 
@@ -1782,14 +1782,14 @@ We can now exploit gauge invariance
 which leaves \(F^{\mu \nu}\) invariant. In particular, we can choose
 the Lorenz gauge <a href="./emf_g_Lg.html#LorenzG">LorenzG</a> here expressed as
 </p>
-<div class="eqlabel" id="org6a52a14">
+<div class="eqlabel" id="orgd1ecd9e">
 <p>
 <a id="LorenzG_4v"></a><a href="./red_rem_Me.html#LorenzG_4v"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgf61a44d">
+<div class="alteqlabels" id="org2d57d58">
 
 </div>
 
@@ -1802,15 +1802,15 @@ the Lorenz gauge <a href="./emf_g_Lg.html#LorenzG">LorenzG</a> here expressed as
 Using the d'Alembertian operator introduced in <a href="./emf_g_Lg.html#dAl">dAl</a>
 here rewritten as
 </p>
-<div class="main div" id="orgf152aad">
-<div class="eqlabel" id="orgf826c45">
+<div class="main div" id="orgf5f60a2">
+<div class="eqlabel" id="org8eca8cc">
 <p>
 <a id="dAl_4v"></a><a href="./red_rem_Me.html#dAl_4v"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orgea79545">
+<div class="alteqlabels" id="orgd49431c">
 
 </div>
 
@@ -1827,18 +1827,18 @@ here rewritten as
 we obtain the final form of
 </p>
 
-<div class="core div" id="org7a7f039">
+<div class="core div" id="org6f2c681">
 <p>
 <b>Maxwell's equations</b> <i>(Lorenz gauge, 4-vector notation)</i>
 </p>
-<div class="eqlabel" id="org5b1a56e">
+<div class="eqlabel" id="orgf6c03ed">
 <p>
 <a id="Max_Lor_4v"></a><a href="./red_rem_Me.html#Max_Lor_4v"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 </svg></a>
 </p>
-<div class="alteqlabels" id="orga66f820">
+<div class="alteqlabels" id="org0a813f5">
 
 </div>
 
@@ -1874,7 +1874,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rem_mre.html b/build/red_rem_mre.html
index 23a9de7..88b60fc 100644
--- a/build/red_rem_mre.html
+++ b/build/red_rem_mre.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1622,7 +1622,7 @@ implies the existence of magnetism, and vice-versa.
 <p>
 To illustrate this, we take a simple example
 </p>
-<aside id="org964fb67">
+<aside id="orgab295ea">
 <p>
 See Purcell \&amp; Morin, section 5.9.
 </p>
@@ -1722,7 +1722,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rm.html b/build/red_rm.html
index e214256..dc7a593 100644
--- a/build/red_rm.html
+++ b/build/red_rm.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rm_Mf.html b/build/red_rm_Mf.html
index a237edb..af6f813 100644
--- a/build/red_rm_Mf.html
+++ b/build/red_rm_Mf.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1616,7 +1616,7 @@ Table of contents
 <p>
 Newton's second law remains valid provided we use the relativistic momentum:
 </p>
-<div class="core div" id="org11c93db">
+<div class="core div" id="orge52f1a4">
 <p>
 <b>Newton's law</b> <i>(relativistic case)</i>
 \[
@@ -1626,7 +1626,7 @@ Newton's second law remains valid provided we use the relativistic momentum:
 
 </div>
 
-<div class="example div" id="org4050d88">
+<div class="example div" id="orgab74cfb">
 <p>
 <b>Example: motion under a constant force</b>
 </p>
@@ -1657,7 +1657,7 @@ The particle's world line thus shows <b>hyperbolic motion</b>.
 </p>
 
 
-<figure id="orgd090155">
+<figure id="org9244ff3">
 <object type="image/svg+xml" data="./fig/red/red_motion_under_cst_F.svg" class="org-svg" alt="Relativistic motion under constant force">
 Sorry, your browser does not support SVG.</object>
 
@@ -1726,15 +1726,15 @@ whereas the longitudinal component transforms in a complicated way:
 For the specific case where the particle is instantaneously at rest in
 the original frame, then
 </p>
-<div class="main div" id="org7c7f004">
-<div class="eqlabel" id="org37e2037">
+<div class="main div" id="orge9d30a6">
+<div class="eqlabel" id="orga8b151c">
 <p>
 <a id="Ftr0"></a><a href="./red_rm_Mf.html#Ftr0"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="orgbf7064d">
+<div class="alteqlabels" id="org970f232">
 
 </div>
 
@@ -1755,18 +1755,18 @@ The way to avoid complicated transformation rules is to define a four-vector
 as the derivative of momentum with respect to proper time, which leads to
 the definition of the
 </p>
-<div class="main div" id="orgc529917">
+<div class="main div" id="org8fbba89">
 <p>
 <b>Minkowski force</b>
 </p>
-<div class="eqlabel" id="org24e429b">
+<div class="eqlabel" id="orgd8fe9be">
 <p>
 <a id="MinkF"></a><a href="./red_rm_Mf.html#MinkF"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
 </p>
-<div class="alteqlabels" id="org6498650">
+<div class="alteqlabels" id="orgcd1fb1c">
 
 </div>
 
@@ -1806,7 +1806,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rm_pt.html b/build/red_rm_pt.html
index 28712cc..31b50f2 100644
--- a/build/red_rm_pt.html
+++ b/build/red_rm_pt.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1629,7 +1629,7 @@ and this is called the <b>ordinary velocity</b>.
 The <b>proper velocity</b> is defined as the hybrid-frame quantity
 (distance as measured on the ground) divided by (proper time interval):
 </p>
-<div class="core div" id="org6b9040e">
+<div class="core div" id="orgdf21b26">
 <p>
 <b>Proper velocity</b>
 \[
@@ -1651,7 +1651,7 @@ By adding the zeroth component
 \]
 we can define the
 </p>
-<div class="core div" id="org75d23d9">
+<div class="core div" id="org7aed082">
 <p>
 <b>four-velocity</b> or <b>proper velocity four-vector</b>
 \[
@@ -1699,7 +1699,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_rm_rme.html b/build/red_rm_rme.html
index ade68fb..3e36627 100644
--- a/build/red_rm_rme.html
+++ b/build/red_rm_rme.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1613,7 +1613,7 @@ Table of contents
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 <div class="outline-text-4" id="text-red_rm_rme">
-<div class="core div" id="org1fef50a">
+<div class="core div" id="org5886454">
 <p>
 The <b>relativistic momentum</b> \({\boldsymbol p}\) is defined as
 \[
@@ -1635,7 +1635,7 @@ p^\mu \equiv m \eta^\mu
 <p>
 When the object is stationary, its energy is the
 </p>
-<div class="core div" id="org2cb0822">
+<div class="core div" id="org39fb20a">
 <p>
 <b>Rest energy</b>
 \[
@@ -1648,7 +1648,7 @@ E_{\mbox{rest}} \equiv m c^2.
 When moving, the difference between relativistic and rest energies
 is the
 </p>
-<div class="core div" id="org59d0366">
+<div class="core div" id="org8f5a639">
 <p>
 <b>Kinetic energy</b>
 \[
@@ -1668,7 +1668,7 @@ this to
 <p>
 In a closed system,
 </p>
-<div class="core div" id="orge0a6a35">
+<div class="core div" id="org12fc8dd">
 <p>
 <b>Total relativistic energy and momentum is conserved</b>
 \[
@@ -1702,7 +1702,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_sr.html b/build/red_sr.html
index 2238caf..571dabc 100644
--- a/build/red_sr.html
+++ b/build/red_sr.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1639,7 +1639,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_sr_4v.html b/build/red_sr_4v.html
index a6aa9be..13dd99d 100644
--- a/build/red_sr_4v.html
+++ b/build/red_sr_4v.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1621,7 +1621,7 @@ Table of contents
 \]
 The Lorentz transformation then reads
 </p>
-<div class="core div" id="org2ede351">
+<div class="core div" id="org4deeed2">
 <p>
 <b>Lorentz transformation</b> (motion along \(x\) at velocity \(v\))
   \[
@@ -1657,7 +1657,7 @@ upper index are called <b>contravariant</b>. Their lower-index
 counterparts are called <b>covariant</b> vectors and are obtained by
 using the Minkowski metric \(g_{\mu \nu}\) according to
 </p>
-<div class="main div" id="org1cd4b37">
+<div class="main div" id="orgec16201">
 <p>
 \[
     a_\mu = \sum_{\nu = 0}^3 g_{\mu \nu} a^\nu, \hspace{10mm}
@@ -1673,7 +1673,7 @@ using the Minkowski metric \(g_{\mu \nu}\) according to
 <p>
 <b>Scalar products</b> are defined as the in-product of covariant/contravariant four-vectors,
 </p>
-<div class="main div" id="orgbb985f0">
+<div class="main div" id="org09ecbcd">
 <p>
 \[
     \sum_{\mu = 0}^3 a^\mu b_\mu \equiv a^\mu b_\mu
@@ -1769,7 +1769,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_sr_Lt.html b/build/red_sr_Lt.html
index aaf67a5..c834675 100644
--- a/build/red_sr_Lt.html
+++ b/build/red_sr_Lt.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1670,7 +1670,7 @@ where \(\bar{d}\) is the distance from \({\cal O}\) to \({\cal A}\) at time
 \]
 Solving these relations yields the dictionary for
 </p>
-<div class="core div" id="org65a91be">
+<div class="core div" id="org13c3e73">
 <p>
 <b>Lorentz transformations</b> (motion along \(x\) at velocity \(v\))
 </p>
@@ -1709,7 +1709,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>
 
diff --git a/build/red_sr_p.html b/build/red_sr_p.html
index 395d4c2..92b05a0 100644
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+++ b/build/red_sr_p.html
@@ -1,7 +1,7 @@
 <!DOCTYPE html>
 <html lang="en">
 <head>
-<!-- 2022-03-22 Tue 10:52 -->
+<!-- 2022-03-24 Thu 08:42 -->
 <meta charset="utf-8">
 <meta name="viewport" content="width=device-width, initial-scale=1">
 <title>Pre-Quantum Electrodynamics</title>
@@ -1293,7 +1293,7 @@ Table of contents
 </summary>
 <ul>
 <li>
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
 
 </li>
 
@@ -1648,18 +1648,18 @@ and we get
 \]
 so the time interval in the train is shorter, namely there is a
 </p>
-<div class="core div" id="org04cf730">
+<div class="core div" id="org4bf8fe3">
 <p>
 <b>Time dilation factor</b>
 </p>
-<div class="eqlabel" id="org37dbf9e">
+<div class="eqlabel" id="orgb19e484">
 <p>
 <a id="gamma"></a><a href="./red_sr_p.html#gamma"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 </svg></a>
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+<div class="alteqlabels" id="orgbb53d13">
 
 </div>
 
@@ -1699,7 +1699,7 @@ and thus
 \]
 Using the time dilation relation then gives
 </p>
-<div class="core div" id="orgd363ff1">
+<div class="core div" id="orgdfa4b99">
 <p>
 <b>Lorentz contraction</b>
 \[
@@ -1732,7 +1732,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
 </div>
 <div id="postamble" class="status">
 <p class="author">Author: Jean-Sébastien Caux</p>
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
 <p class="validation"></p>
 </div>