2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93418The effective one-loop potential on $R^{m+1}\times S^N$ spaces for massless tensor fields is evaluated. The Casimir energy is given as a value of $ζ-$ function by means of which regularization is made. In even- dimensional spaces the vacuum energy contains divergent terms coming from poles of $ζ(s,q)$ at $s=1$, whereas in odd-dimensional spaces it becomes finite.LaTex, 4 pages. Published in the Proceedings of the Int. Seminar "Path Integrals and Applications"Quantum Physicstext