Local effects of the quantum vacuum in Lorentz-violating electrodynamics

TL;DR

This paper investigates how Lorentz violation in the minimal standard model extension affects the Casimir force between parallel plates, using a local Green's function approach and perturbation theory to compute vacuum stresses and energies.

Contribution

It introduces a perturbative method to analyze Lorentz violation effects on the Casimir force using Green's functions and local stress-energy tensor calculations.

Findings

Lorentz violation modifies the local vacuum stress between plates.

The renormalized Casimir force is computed analytically.

Local Casimir energy diverges near plates but does not affect the force.

Abstract

The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum stress, which is obtained as the difference between the vacuum stress in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum stress. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.