The classical and quantum photon field for non-compact manifolds with boundary and in possibly inhomogeneous media
arXiv:2011.12601 · doi:10.1007/s00220-021-04218-4
Abstract
In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary and in possibly inhomogeneous media. Such a construction is complicated by the presence of zero-modes that may appear in the presence of non-trivial topology of the manifold or the boundary. An important special case is with obstacles. In this case the zero modes have a direct interpretation in terms of the topology of the obstacle. I give a formula for the renormalised stress energy tensor in terms of an integral kernel of an operator defined by spectral calculus of the Laplace Beltrami operator on differential forms with relative boundary conditions.
arXiv comment32 pages, 2 figures, subtantial revision
References in corpus (10)
- Microlocal Analysis and Interacting Quantum Field Theories: Renormalization on Physical Backgrounds
- A Quantum Weak Energy Inequality for Spin-One Fields in Curved Spacetime
- Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
- Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples
- Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium
- Gupta-Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times
- Quantization of the Maxwell field in curved spacetimes of arbitrary dimension
- The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem and its applications
- Quantum Energy Inequalities in Pre-Metric Electrodynamics
- A mathematical analysis of Casimir interactions I: The scalar field