Gauge Invariance in Classical Electrodynamics

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Scientific Paper
Title Gauge Invariance in Classical Electrodynamics
Author(s) Wolfgang Engelhardt
Keywords {{{keywords}}}
Published 2005
Journal Annales de la Fondation Louis de Broglie
Volume 30
Number 2
Pages 157-178


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.