The Casimir energy of a massive fermionic field confined in a d+1 dimensional slab-bag

TL;DR

This paper calculates the Casimir energy for a massive fermionic field in a d+1 dimensional slab with MIT bag boundary conditions, providing a simple method applicable to various boundary setups.

Contribution

It introduces a straightforward approach to sum zero-point energies for quantum fields with arbitrary boundary conditions on flat surfaces.

Findings

Analytic expressions for Casimir energy in different mass limits.

Method matches known results in specific cases.

Extension potential to other boundary configurations.

Abstract

We evaluate the fermionic Casimir effect associated with a massive fermion confined within a planar (d+1) dimensional slab-bag, on which MIT bag model boundary conditions of standard type, along a single spatial direction, are imposed. A simple and effective method for adding up the zero-point energy eigenvalues, corresponding to a quantum field under the influence of arbitrary boundary conditions, imposed on the field on flat surfaces perpendicular to a chosen spatial direction, is proposed. Using this procedure, an analytic result is obtained, from which small and large fermion mass limits, valid for an arbitrary number of dimensions, are derived. They match some known results in particular cases. The method can be easily extended to other configurations.