# Symmetry in Electrodynamics: From Special to General Relativity, Macro to Quantum Domains

- Myron W. Evans

Published Online: 13 MAR 2002

DOI: 10.1002/0471231479.ch11

Copyright © 2001 John Wiley & Sons, Inc.

Book Title

## Modern Nonlinear Optics, Part I, Volume 119, Second Edition

Additional Information

#### How to Cite

Sachs, M. (2001) Symmetry in Electrodynamics: From Special to General Relativity, Macro to Quantum Domains, in Modern Nonlinear Optics, Part I, Volume 119, Second Edition (ed M. W. Evans), John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471231479.ch11

#### Publication History

- Published Online: 13 MAR 2002
- Published Print: 28 SEP 2001

#### Book Series:

#### Book Series Editors:

- I. Prigogine
^{2,3}and - Stuart A. Rice
^{4}

#### Series Editor Information

- 2
Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas, USA

- 3
International Solvay Institutes, Université Libre de Bruxelles, Brussels, Belgium

- 4
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois, USA

#### ISBN Information

Print ISBN: 9780471389309

Online ISBN: 9780471231479

- Summary
- Chapter

### Keywords:

- symmetry;
- electrodynamics;
- electromagnetic potential;
- Maxwell's equations;
- spinor form;
- electromagnetic field theory;
- general relativity;
- wave mechanics

### Summary

The chapter begins with a brief review of the theory of electromagnetism based on its underlying symmetry in relativity theory. Section II presents an outline of the generalization of the vector potential of electromagnetic theory so as to include a gauge-invariant Pseudovector part. This is allowed because of the lack of reflection symmetry in the relativity groups. Section III presents the full forms of the equations of electrodynamics in terms of the irreducible representations of the Lie groups of relativity theory. It is a two-component spinor formalism that follows from a factorization of the standard vector representation of the Maxwell formalism. In Section IV the theory is extended to its full form in general relativity. It is demonstrated that by removing the reflection symmetry elements from the underlying group of general relativity, one arrives at the factorized field equations that fully unify the gravitational features of matter in terms of Einstein's field equations with the electromagnetic features of matter in terms of the Maxwell field equations. Section V demonstrates that the quaternion structure of the fields that correspond to the electromagnetic field tensor and its current density source, implies a very important consequence for electromagnetism. It is that the local limit of the time component of the four-current density yields a derived normalization.