Fermionic Casimir effect at finite temperature in Horava-Lifshitz theories

TL;DR

This paper analyzes the finite temperature Casimir effect for a Lorentz-violating massless fermion field in Horava-Lifshitz theories, deriving analytic expressions for free energy and pressure under various conditions.

Contribution

It provides the first detailed analytic study of the fermionic Casimir effect at finite temperature within Horava-Lifshitz frameworks, considering Lorentz violation and boundary conditions.

Findings

Derived explicit formulas for Helmholtz free energy and Casimir pressure.

Analyzed effects of Lorentz violation parameter and temperature limits.

Provided results for different boundary and temperature scenarios.

Abstract

In this work, I study the finite temperature Casimir effect due to a massless fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I investigate a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this study using the generalized zeta function technique that enables me to obtain the Helmholtz free energy and the Casimir pressure when the Casimir plates are in thermal equilibrium with a heat reservoir at finite temperature. I investigate the cases when the parameter associated with the violation of Lorentz invariance is even or odd and the limits of low and high temperature relative to the inverse of plate distance, examining all possible combinations of the above quantities. In all scenarios studied, I obtain simple and accurate analytic expressions of the free energy and the temperature-dependent Casimir pressure.