The Role of Mass and External Field on the Fermionic Casimir Effect

TL;DR

This paper investigates how fermion mass and external fields influence the fermionic Casimir energy in a specific topology, using advanced regularization techniques to obtain exact results.

Contribution

It introduces a novel approach combining alpha-representation and Euler-Maclaurin formula to exactly compute fermionic Casimir energies considering mass and external fields.

Findings

Fermion mass significantly affects Casimir energy density.

External fields modify the Casimir effect in the studied topology.

Exact analytical expressions are derived for different spin connection conditions.

Abstract

The aim of this work is to investigate the role played by the fermion mass and that of an external field on the fermionic Casimir energy density under S^1 X R^3 topology. Both twisted and untwisted spin connections are considered and the exact calculation is performed using a somewhat different approach based on the combination of the analytic regularization method through alpha-representation and Euler-Maclaurin summation formula.