Gauge-free Electrodynamics

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.