2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51562The 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.LaTex file, 13 pages, no figuresHigh Energy Physics - Theorytext