Green's Function expansion of scalar and vector fields in the presence of a medium

TL;DR

This paper develops a Green's function series expansion for scalar and electromagnetic fields in media, providing a canonical, functional-integral approach that generalizes to finite temperature and covariant formulations.

Contribution

It introduces a novel series expansion method for Green's functions in media, extending to electromagnetic fields and finite-temperature scenarios.

Findings

Series expansion for scalar Green's function in media

Expression for Lifshitz energy in terms of medium susceptibility

Covariant formulation applicable to electromagnetic fields

Abstract

Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms of the susceptibility of the medium is derived and the whole formalism is generalized to the case of electromagnetic field in the presence of some dielectrics. A covariant formulation of the problem is presented.