Fermionic Casimir Effect at Finite Temperature in Hořava-Lifshitz Theories

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.