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

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.