Casimir Energy of Massless Fermions in the Slab-bag

TL;DR

This paper calculates the Casimir energy of massless fermions between parallel plates in arbitrary dimensions, using a combined regularization method to obtain finite results.

Contribution

It introduces a novel regularization approach combining dimensional and zeta-function techniques for fermionic Casimir energy calculations.

Findings

Finite zero-point energy density for any number of dimensions.

General expression for fermionic Casimir energy in slab geometry.

Regularization method ensures finiteness of energy in arbitrary dimensions.

Abstract

The zero-point energy of a massless fermion field in the interior of two parallel plates in a D-dimensional space-time at zero temperature is calculated. In order to regularize the model, a mix between dimensional and zeta-function regularization procedure is used and it is found that the regularized zero-point energy density is finite for any number of space-time dimensions. We present a general expression for the Casimir energy for the fermionic field in such a situation.