We present an overview of Maxwell’s equations in covariant form, aimed at the undergraduate familiar with the vector formalism of electrodynamics. We motivate this project with the tenets of special relativity and deploy complete tensor derivations to aid in mathematical understanding. We demonstrate that Maxwell’s theory naturally lends itself to covariant formalism.

1.
T.
Moore
,
Laws of Physics are Frame-Independent
(
McGraw-Hill
,
New York, NY
,
2017
), p. 95.
Google Scholar
 
2.
R.
Gambini
 and
J.
Pullin
,
A First Course in Loop Quantum Gravity
(
Oxford University Press
,
New York
,
2011
), pp.
8
–
21
.
Google Scholar
Crossref
Search ADS
 
3.
S.
Carroll
,
Spacetime and Geometry An Introduction to General Relativity
(
Addison-Wesley
,
San Francisco, CA
,
2004
),
pp.
29
–
30
.
Google Scholar
 
4.
R.
Feynman
,
Quantum Electrodynamics
(
Addison-Wesley
,
Reading, MA
,
1998
), p.
26
.
Google Scholar
 
5.
J.
Baez
 and
J.
Muniain
,
Gauge Fields, Knots and Gravity
(
World Scientific
,
Hackensack, NJ
,
1994
), p.
viii
.
Google Scholar
 
6.
T.
Moore
,
A General Relativity Workbook
(
University Science Books
,
Mill Valley, CA
,
2013
), pp.
13
–
76
.
Google Scholar
 
This content is only available via PDF.
© 2024 Author(s).
2024
Author(s)
Published by AIP Publishing.