  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.

General Physics