Casimir effect of a doubly Lorentz-violating scalar in magnetic field

TL;DR

This paper investigates how a doubly Lorentz-violating scalar field, influenced by a magnetic field and boundary conditions, affects the Casimir effect, providing explicit formulas in various asymptotic regimes.

Contribution

It introduces a comprehensive analysis of the Casimir effect for a Lorentz-violating scalar field with a magnetic field, considering multiple vector orientations and boundary conditions.

Findings

Explicit formulas for Casimir energy and pressure in different limits.

Effects of Lorentz violation on the Casimir force.

Impact of magnetic field orientation on the Casimir effect.

Abstract

In this work I study the Casimir effect caused by a charged and massive scalar field that violates Lorentz symmetry in an aether-like and CPT even manner, by direct coupling between the field derivatives and two fixed orthogonal unit vectors. I call this a "double" Lorentz violation. The field will satisfy either Dirichlet or mixed boundary conditions on a pair of plane parallel plates. I use the generalized zeta function technique to examine the effect of a uniform magnetic field, perpendicular to the plates, on the Casimir energy and pressure. Three different pairs of mutual directions of the unit vectors are possible: timelike and spacelike perpendicular to the magnetic field, timelike and spacelike parallel to the magnetic field, spacelike perpendicular and spacelike parallel to the magnetic field. I fully examine all of them for both types of boundary conditions listed above and, in all cases and for both types of boundary conditions, I obtain simple expressions of the zeta function, Casimir energy and pressure in the three asymptotic limits of strong magnetic field, large mass, and small plate distance.