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

FRANCHINO-VIÑAS, S.A.; MANTIÑAN, M.N.; MAZZITELLI, F.D.

Physical Review D

American Physical Society

Año: 2022 vol. 105

2470-0010

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.