Thermal effects on the Casimir energy of a Lorentz-violating scalar in magnetic field

TL;DR

This paper analyzes how finite temperature, magnetic fields, and Lorentz symmetry breaking affect the Casimir energy of a charged scalar field with boundary conditions, providing analytic expressions for various asymptotic regimes.

Contribution

It introduces a detailed analysis of the thermal Casimir effect for Lorentz-violating scalar fields under magnetic fields, considering different symmetry-breaking directions and boundary conditions.

Findings

Thermal corrections depend strongly on Lorentz symmetry breaking direction.

Analytic expressions for Casimir energy and pressure are derived for various regimes.

The effects vary with magnetic field strength, temperature, and mass asymptotics.

Abstract

In this work I investigate the finite temperature Casimir effect due to a massive and charged scalar field that breaks Lorentz invariance in a CPT-even, aether-like way. I study the cases of Dirichlet and mixed (Dirichlet-Neumann) boundary conditions on a pair of parallel plates. I will not examine the case of Neumann boundary conditions since it produces the same results as Dirichlet boundary conditions. The main tool used in this investigation is the $\zeta$-function technique that allows me to obtain the Helmoltz free energy and Casimir pressure in the presence of a uniform magnetic field perpendicular to the plates. Three cases of Lorentz asymmetry are studied: timelike, spacelike and perpendicular to the magnetic field, spacelike and parallel to the magnetic field. Asymptotic cases of small plate distance, high temperature, strong magnetic field, and large mass will be considered for each of the three types of Lorentz asymmetry and each of the two types of boundary conditions examined. In all these cases simple and very accurate analytic expressions of the thermal corrections to the Casimir energy and pressure are obtained and I discover that these corrections strongly depend on the direction of the unit vector that produces the breaking of the Lorentz symmetry.