Potential Theory in Classical Electrodynamics
arXiv:1209.3449
Abstract
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday's law of induction and Maxwell's flux law. As a consequence of this internal contradiction there is neither gauge invariance, nor exist unique solutions in general. It is also demonstrated that inhomogeneous wave equations cannot be solved by retarded integrals.
8 pages, 1 figure, LaTeX. Simplified argument in section 2 suggested by Dr. Peter Enders (see Acknowledgments). Expanded argument in section 4. Results unchanged