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In this article I give a rigorous construction of the classical and quantumphoton field on non-compact manifolds with boundary and in possiblyinhomogeneous media. Such a construction is complicated by the presence ofzero-modes that may appear in the presence of non-trivial topology of themanifold or the boundary. An important special case is $\mathbb{R}^3$ withobstacles. In this case the zero modes have a direct interpretation in terms ofthe topology of the obstacle. I give a formula for the renormalised stressenergy tensor in terms of an integral kernel of an operator defined by spectralcalculus of the Laplace Beltrami operator on differential forms with relativeboundary conditions.

The classical and quantum photon field for non-compact manifolds with boundary and in possibly inhomogeneous media