Gauge Invariance in Classical Electrodynamics
| Scientific Paper | |
|---|---|
| Title | Gauge Invariance in Classical Electrodynamics |
| Read in full | Link to paper (Internet Archive) |
| Author(s) | Wolfgang Engelhardt |
| Keywords | classical electrodynamics, invariance, electromagnetic field, Maxwell's Equations |
| Published | 2005 |
| Journal | Annales de la Fondation Louis de Broglie |
| Volume | 30 |
| Number | 2 |
| Pages | 157-178 |
Read the full paper here (archived copy — the original link is no longer available)
Abstract
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uniqueness is not justified. The reason for this failure is traced back to the inhomogeneous wave equations which connect the propagating fields and their sources at the same time.