Magnetic corrections to the fermionic Casimir effect in Horava-Lifshitz theories

TL;DR

This paper explores how a magnetic field influences the Casimir effect for a massless, charged fermion field that violates Lorentz invariance within Horava-Lifshitz theories, providing analytic expressions for energy and pressure.

Contribution

It introduces a detailed analysis of magnetic corrections to the fermionic Casimir effect in Lorentz-violating Horava-Lifshitz theories using the ζ-function technique.

Findings

Derived analytic formulas for Casimir energy and pressure under magnetic fields.

Analyzed effects for different Lorentz violation parameters and magnetic field strengths.

Provided accurate expressions applicable to various boundary conditions and field configurations.

Abstract

In this paper I investigate the effect of a magnetic field on the Casimir effect due to a massless and charged fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I focus on the case of a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this investigation using the $\zeta$-function technique that allows me to obtain Casimir energy and pressure in the presence of a uniform magnetic field orthogonal to the plates. I investigate the cases of the parameter associated with the violation of Lorentz invariance being even or odd and the cases of weak and strong magnetic field, examining all possible combinations of the above quantities. In all cases I obtain simple and very accurate analytic expressions of the magnetic field dependent Casimir energy and pressure.