  We propose a reformulation of electrodynamics in terms of a {\it physical}
vector potential entirely free of gauge ambiguities. Quantizing the theory
leads to a propagator that is gauge invariant by construction in this
reformulation, in contrast to the standard photon propagator. Coupling the
theory to a charged Abelian Higgs field leads at the quantum level to a one
loop effective potential which realizes the Coleman-Weinberg mechanism of mass
generation, thus resolving the issue of its gauge dependence. We relate our
results to recent work by Niemi et. al. and Faddeev, where similar strategies
are adopted in a version of the electroweak theory. Other theories with linear
Abelian gauge invariance, like the linearized spin 2 theory of gravity or the
antisymmetric tensor field, which may all be reformulated in terms of physical
vector or tensor potentials without gauge ambiguities, are also discussed
briefly.
