Integral Formulation of the Macroscopic Quantum Electrodynamics in Dispersive Dielectric Objects

We present an integral formulation of the macroscopic quantum electrodynamics in linear dispersive dielectric objects of finite sizes using the Hopfield-type approach. We introduce an integral equation for the polarization density field operator in the Heisenberg picture, based on the retarded Green's function for the vacuum, and we express the electromagnetic field operators as function of the polarization operator. The proposed formulation is particularly attractive because it enables the direct application of consolidated repertory in computational classical electrodynamics to carry out quantum electrodynamics computation in open, dispersive, and absorbing environments.