Finite Temperature Casimir Effect for Massless Majorana Fermions in a Magnetic Field

TL;DR

This paper uses zeta function regularization to analyze the finite temperature Casimir effect for massless Majorana fermions between plates under a magnetic field, deriving accurate formulas for free energy and pressure.

Contribution

It provides exact all-order expressions for the Casimir effect of Majorana fermions in magnetic fields at finite temperature, including weak and strong field limits.

Findings

Derived exact zeta function expressions for the system.

Obtained simple analytic formulas for free energy and pressure.

Validated formulas across all temperature and distance ranges.

Abstract

The zeta function regularization technique is used to study the finite temperature Casimir effect for a massless Majorana fermion field confined between parallel plates and satisfying bag boundary conditions. A magnetic field perpendicular to the plates is included. An expression for the zeta function is obtained, which is exact to all orders in the magnetic field strength, temperature and plate distance. The zeta function is used to calculate the Helmholtz free energy of the Majorana field and the pressure on the plates, in the case of weak magnetic field and strong magnetic field. In both cases, simple analytic expressions are obtained for the free energy and pressure which are very accurate and valid for all values of the temperature and plate distance.