A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

TL;DR

This paper presents a non-perturbative analytical method to evaluate the scalar Casimir effect considering Lorentz symmetry violation, revealing how Lorentz-violating parameters modify the Casimir energy, force, and energy density.

Contribution

It introduces a closed-form, non-perturbative approach to compute the Casimir effect with Lorentz violation using Green's functions, extending understanding beyond perturbative methods.

Findings

Casimir energy and force are modified by Lorentz-violating parameters.

The Casimir force scales with the determinant of the Lorentz-violation tensor.

Finite-temperature effects on the Casimir stress are also analyzed.

Abstract

We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance $L$, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor $h^{\,\mu\nu}$ that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that $\mathcal{F}_c(L)=\mathcal{F}_0(\tilde{L})/\sqrt{-{\rm det}\, h^{\,\mu\nu}}$, where $\mathcal{F}_0$ is the Lorentz-invariant expression, and $\tilde{L}$ is the plate separation rescaled by the component of $h^{\,\mu\nu}$ normal to the plates, $\tilde{L}=L/\sqrt{-h^{nn}}$. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.