Quantum Electromagnetic Stress Tensor in an Inhomogeneous Medium

TL;DR

This paper investigates the electromagnetic stress tensor in an inhomogeneous medium with a spatially varying permittivity, analyzing divergences, singularities, and renormalization issues relevant to quantum field theory in complex materials.

Contribution

It extends the analysis of vacuum stress tensors to inhomogeneous media with spatially varying permittivity, highlighting universal divergence and singularity structures.

Findings

Divergences regulated by point-splitting methods

Universal character of divergences for TE and TM modes

Singularities at dielectric-vacuum interfaces depending on material discontinuities

Abstract

Continuing a program of examining the behavior of the vacuum expectation value of the stress tensor in a background which varies only in a single direction, we here study the electromagnetic stress tensor in a medium with permittivity depending on a single spatial coordinate, specifically, a planar dielectric half-space facing a vacuum region. There are divergences occurring that are regulated by temporal and spatial point-splitting, which have a universal character for both transverse electric and transverse magnetic modes. The nature of the divergences depends on the model of dispersion adopted. And there are singularities occurring at the edge between the dielectric and vacuum regions, which also have a universal character, depending on the structure of the discontinuities in the material properties there. Remarks are offered concerning renormalization of such models, and the significance of the stress tensor. The ambiguity in separating "bulk" and "scattering" parts of the stress tensor is discussed.