Thermal corrections to the Casimir energy in a Lorentz-breaking scalar field theory

TL;DR

This paper studies how temperature and Lorentz symmetry breaking affect the Casimir energy of a scalar field confined between plates, providing detailed analysis across various physical regimes.

Contribution

It introduces a method to compute thermal Casimir energy in a Lorentz-breaking scalar field theory considering finite temperature and chemical potential.

Findings

Thermal effects significantly modify the Casimir energy.

Results depend on mass, temperature, and plate separation regimes.

The approach can be extended to other Lorentz-violating field theories.

Abstract

In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel-Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between the plates and temperature.