On the computation of Casimir stresses in open media and Lifshitz theory

TL;DR

This paper presents a direct, self-contained method for computing Casimir stresses in open media using Lifshitz theory, avoiding complex regularization techniques and focusing on electromagnetic mode analysis.

Contribution

It introduces a novel approach to derive Casimir stresses in open dielectric systems directly from Maxwell equations without mode regularization or Krein formula reliance.

Findings

Derived regular expressions for Casimir stresses in open media.

Expressed stresses as double integrals over real or imaginary frequencies.

Provided a self-contained methodology applicable to various open systems.

Abstract

A classification of the electromagnetic modes on open and closed spatial domains containing media with piecewise homogeneous permittivities is used to facilitate the derivation of quantum induced Casimir stresses in dielectrics. By directly exploiting the complex analytic properties of solutions of the macroscopic Maxwell equations for open systems it is shown how regular expressions for such stresses can be expressed in terms of double integrals involving either real or pure imaginary frequencies associated with harmonic modes in conformity with the Lifshitz theory for separated planar dielectric half-spaces. The derivation is self-contained without recourse to the Krein formula for a density of states or mode regularization and offers a more direct approach to other open systems.