  The aim of this paper is to prove the existence of Hadamard states for the
Maxwell equations on any globally hyperbolic spacetime. This will be achieved
by introducing a new gauge fixing condition, the Cauchy radiation gauge, that
will allow to suppress all the unphysical degrees of freedom. The key
ingredient for achieving this gauge is a new Hodge decomposition for
differential k-forms in Sobolev spaces on complete (possibly non-compact)
Riemannian manifolds.
