Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries

A form of quantum electrodynamics is developed which allows us to treat a number of problems involving dielectric and conducting surfaces, the presence of which leads to a number of new observable effects. A number of suitably defined response functions play a basic role in the present approach, as these in conjunction with the fluctuation-dissipation theorem lead to electromagnetic field correlation functions, which describe physical effects such as lifetimes, frequency shifts of the excited states, dispersion forces, etc. The quantization of the electromagnetic field is only implicitly used. A large part of the present paper is devoted to the calculation of the response functions involving different geometries and various types of dielectrics. Both spatially dispersive and spatially nondispersive dielectrics are considered. The response functions are calculated using Maxwell's equations and the usual boundary conditions at the interface adjoining the two mediums. As a first application of the present approach, the black-body fluctuations in finite geometries and the influence of surfaces on its temporal and spatial coherence are studied. An interesting theorem is also proved which enables us to calculate the normally ordered (antinormally ordered) correlation functions from the symmetrized correlation functions.