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Update 2022-03-24 08:43

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Jean-Sébastien
2022-03-24 08:43:21 +01:00
parent 1d852e7213
commit 50704eba07
211 changed files with 1506 additions and 3143 deletions
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build/ems_ms_vp_LC.html
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@@ -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">
<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="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">
<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="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">
<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="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>