Quantum electrodynamics of inhomogeneous anisotropic media

TL;DR

This paper develops a comprehensive quantum electrodynamics framework for inhomogeneous, anisotropic media, deriving key physical quantities and discussing gauge invariance, with implications for Casimir physics in nonequilibrium conditions.

Contribution

It provides a general expression for the electromagnetic influence action in complex media and evaluates the generating functional, energy, and Poynting vector considering initial conditions and matter degrees of freedom.

Findings

Derived closed-form expressions for energy, Poynting vector, and Maxwell tensor.

Analyzed gauge invariance issues in inhomogeneous anisotropic media.

Discussed implications for Casimir physics in nonequilibrium scenarios.

Abstract

In this work we calculate the closed time path (CTP) generating functional for the electromagnetic (EM) field interacting with inhomogeneous anisotropic matter. For this purpose, we first find a general expression for the electromagnetic field's influence action from the interaction of the field with a composite environment consisting in the quantum polarization degrees of freedom in each point of space, at arbitrary temperatures, connected to thermal baths. Then, we evaluate the generating functional for the gauge field, in the temporal gauge, by implementing the Faddeev-Popov procedure. Finally, through the point-splitting technique, we calculate closed expressions for the energy, the Poynting vector and the Maxwell tensor in terms of the Hadamard propagator. We show that all the quantities have contributions from the field's initial conditions and also from the matter degrees of freedom. Throughout the whole work we discuss and give insights about how the gauge invariance must be treated in the formalism when the EM field is interacting with inhomogeneous anisotropic matter. We study the electrodynamics in the temporal gauge, obtaining the EM field's equation and a residual condition. Finally analyze the case of the EM field in bulk material and also discuss several general implications of our results in relation with the Casimir physics in a nonequilibrium scenario.