Evaluation of Vacuum Energy for Tensor Fields on Spherical Spaces

Abstract

The 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 $\zeta -$ function by means of which regularization is made. In even- dimensional spaces the vacuum energy contains divergent terms coming from poles of $\zeta (s,q)$ 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"