The finite vacuum energy for spinor, scalar and vector fields

TL;DR

This paper calculates the one-loop Casimir energy for scalar, spinor, and vector fields on specific product spaces, exploring divergence cancellation and comparing results with existing literature.

Contribution

It provides explicit calculations of vacuum energy for various fields on product manifolds and discusses divergence cancellation methods.

Findings

Divergent parts of Casimir energy can be canceled in even-dimensional spaces.

Results include explicit formulas for vacuum energy on $R^{m+1} imes Y$ spaces.

Comparison with previous literature validates some of the computed energies.

Abstract

We compute the one-loop potential (the Casimir energy) for scalar, spinor and vectors fields on the spaces $\,R^{m+1}\, \times\,Y$ with $\,Y=\,S^N\,,CP^2$. As a physical model we consider spinor electrodynamics on four-dimensional product manifolds. We examine the cancelation of a divergent part of the Casimir energy on even-dimensional spaces by means of including the parameter $\,M$ in original action. For some models we compare our results with those found in the literature.