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<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-08 Tue 17:21 -->
<!-- 2022-02-09 Wed 07:31 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1616,7 +1616,7 @@ Table of contents
</ul>
</details>
</nav>
<ul class="navigation-links"><li>Prev:&nbsp;<a href="red_rem_Fmunu.html">The Field Tensor&emsp;<small>[red.rem.Fmunu]</small></a></li><li>Next:&nbsp;<a href="qed.html">Quantum Electrodynamics&emsp;<small>[qed]</small></a></li><li>Up:&nbsp;<a href="red_rem.html">Relativistic Electromagnetism&emsp;<small>[red.rem]</small></a></li></ul><div id="outline-container-red_rem_Me" class="outline-4">
<ul class="breadcrumbs"><li><a class="breadcrumb-link"href="red.html">Relativistic Electrodynamics</a></li><li><a class="breadcrumb-link"href="red_rem.html">Relativistic Electromagnetism</a></li><li>Maxwell's Equations in Relativistic Notation</li></ul><ul class="navigation-links"><li>Prev:&nbsp;<a href="red_rem_Fmunu.html">The Field Tensor&emsp;<small>[red.rem.Fmunu]</small></a></li><li>Next:&nbsp;<a href="qed.html">Quantum Electrodynamics&emsp;<small>[qed]</small></a></li><li>Up:&nbsp;<a href="red_rem.html">Relativistic Electromagnetism&emsp;<small>[red.rem]</small></a></li></ul><div id="outline-container-red_rem_Me" class="outline-4">
<h4 id="red_rem_Me">Maxwell's Equations in Relativistic Notation<a class="headline-permalink" href="./red_rem_Me.html#red_rem_Me"><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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@@ -1646,7 +1646,7 @@ 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="org880d382">
<div class="core div" id="orgb04fcdf">
<p>
{\bf Current density 4-vector}
\[
@@ -1659,7 +1659,7 @@ Recognizing the proper velocity, we thus get that charge density and current den
<p>
The continuity equation (\ref{eq:continuity}) takes the simple form
</p>
<div class="core div" id="orge750de3">
<div class="core div" id="orgd67b414">
<p>
{\bf Continuity equation}
\[
@@ -1671,7 +1671,7 @@ The continuity equation (\ref{eq:continuity}) takes the simple form
<p>
while similarly the notation simplifies for
</p>
<div class="main div" id="org08f0a21">
<div class="main div" id="org39ea8b8">
<p>
{\bf Maxwell's equations}
\[
@@ -1686,7 +1686,7 @@ while similarly the notation simplifies for
<p>
In terms of \(F^{\mu \nu}\) and the proper velocity \(\eta^\mu\), we also have the
</p>
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<div class="main div" id="org5c9b443">
<p>
{\bf Minkowski force on a charge \(q\)}
\[
@@ -1736,7 +1736,7 @@ the Lorenz gauge (\ref{eq:InhomogeneousMaxwellLorenzGauge}) here expressed as
\]
Defining the
</p>
<div class="main div" id="org60385bf">
<div class="main div" id="org9963f2a">
<p>
{\bf d'Alembertian operator}
\[
@@ -1749,7 +1749,7 @@ Defining the
we obtain the final form of
</p>
<div class="core div" id="org1ba8f7d">
<div class="core div" id="org47df391">
<p>
{\bf Maxwell's equations (Lorenz gauge, 4-vector notation)}
\[
@@ -1766,10 +1766,21 @@ of these equations.
</div>
<hr><div id="postamble" class="status">
<hr>
<div class="license">
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
target="_blank" class="m-2">
<img alt="Creative Commons License" style="border-width:0"
src="https://licensebuttons.net/l/by/4.0/80x15.png"/>
</a>
Except where otherwise noted, all content is licensed under a
<a rel="license noopener" href="https://creativecommons.org/licenses/by/4.0/"
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: 2022-02-08 Tue 17:21</p>
<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
<p class="date">Created: 2022-02-09 Wed 07:31</p>
<p class="validation"></p>
</div>