Casimir effect of a Lorentz-violating scalar in magnetic field

TL;DR

This paper investigates how Lorentz-violating scalar fields influence the Casimir effect under magnetic fields, deriving analytic expressions for energy and pressure variations based on symmetry breaking directions.

Contribution

It provides the first analytic expressions for Casimir energy and pressure for Lorentz-violating scalar fields with magnetic fields under various symmetry-breaking scenarios.

Findings

Casimir energy and pressure depend on Lorentz symmetry breaking direction.

Magnetic corrections significantly alter Casimir forces.

Analytic formulas derived for small distances, strong fields, and large masses.

Abstract

In this paper I study the Casimir effect caused by a charged and massive scalar field that breaks Lorentz invariance in a CPT-even, aether-like manner. I investigate the case of a scalar field that satisfies Dirichlet or mixed (Dirichlet-Neumann) boundary conditions on a pair of very large plane parallel plates. The case of Neumann boundary conditions is straightforward and will not be examined in detail. I use the $\zeta$-function regularization technique to study the effect of a constant magnetic field, orthogonal to the plates, on the Casimir energy and pressure. I investigate the cases of a timelike Lorentz asymmetry, a spacelike Lorentz asymmetry in the direction perpendicular to the plates, and a spacelike asymmetry in the plane of the plates and, in all those cases, derive simple analytic expressions for the zeta function, Casimir energy and pressure in the limits of small plate distance, strong magnetic field and large scalar field mass. I discover that the Casimir energy and pressure, and their magnetic corrections, all strongly depend on the direction of the unit vector that implements the breaking of the Lorentz symmetry.