The Classical and Quantum Photon Field for Non-compact Manifolds with Boundary and in Possibly Inhomogeneous Media

In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary in possibly inhomogeneous media. Such is complicated by presence zero-modes that may appear non-trivial topology manifold or boundary. An important special case $\mathbb{R}^3$ obstacles. zero modes have direct interpretation terms obstacle. formula for renormalised stress energy tensor an integral kernel operator defined spectral calculus Laplace Beltrami differential forms relative conditions.