Towards a heat kernel expansion for the electromagnetic field interacting with a dielectric body of arbitrary form

Abstract

The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of their applicability to the electromagnetic field interacting with dielectric body of arbitrary form. Using the toy-model of scalar photons we develop multiple reflection expansion method which seems the most promising one when the field obeys dielectric-like matching conditions on an arbitrary interface and show that the heat kernel coefficients are expressible through geometric invariants of the latter.