Quantum vacuum fluctuations and the principle of virtual work in inhomogeneous backgrounds

TL;DR

This paper investigates the stress-energy tensor of a quantum scalar field in inhomogeneous backgrounds, providing formal expressions, proving the principle of virtual work for Casimir forces, and analyzing divergences with perturbative and WKB methods.

Contribution

It offers the first all-order formal expressions for the stress-energy tensor in inhomogeneous backgrounds and explicitly proves the principle of virtual work for Casimir forces.

Findings

Explicit all-order formal expressions for stress-energy tensor.

Proof of the principle of virtual work for Casimir forces.

Analysis of divergences in inhomogeneous backgrounds.

Abstract

We discuss several aspects of the stress-energy tensor for a quantum scalar field in an inhomogeneous background, the latter being modeled by a variable mass. Using a perturbative approach, dimensional regularization and adiabatic subtraction, we present all-order formal expressions for the stress-energy tensor. Importantly, we provide an explicit proof of the principle of virtual work for Casimir forces, taking advantage of the conservation law for the renormalized stress-energy tensor. We discuss also discontinuity-induced divergences. For the particular case of planar inhomogeneities, we corroborate the perturbative results with a WKB-inspired expansion.