Path integral quantization of electrodynamics in dielectric media

TL;DR

This paper develops a path integral quantization method for electrodynamics in inhomogeneous dielectric media, incorporating all photon polarizations and ghost fields, and analyzes divergences using heat kernel techniques.

Contribution

It introduces a comprehensive quantization approach for electrodynamics in dielectric media, including ghost fields and divergence analysis with heat kernel methods.

Findings

No cancellation between ghosts and non-physical photon degrees of freedom.

Explicit expressions for heat kernel coefficients in dielectric media.

Identification of ultraviolet divergences in the effective action.

Abstract

In the present paper we study the Faddeev-Popov path integral quantization of electrodynamics in an inhomogenious dielectric medium. We quantize all polarizations of the photons and introduce the corresponding ghost fields. Using the heat kernel technique, we express the heat kernel coefficients in terms of the dielectricity $\epsilon (x)$ and calculate the ultra violet divergent terms in the effective action. No cancellation between ghosts and "non-physical" degrees of freedom of the photon is observed.