Stress tensor for massive fields on flat spaces of spatial topology R^2\times{S^1}

TL;DR

This paper computes the energy-momentum tensor for massive scalar and spinor fields on flat spaces with non-trivial topology, revealing new results and differences from massless cases in specific limits.

Contribution

It provides new calculations of the energy-momentum tensor for massive fields on a flat space with S^1 topology, extending previous results and highlighting qualitative differences from massless fields.

Findings

Results on the first space confirm existing literature.

Results on the second space are novel.

Differences between massless and massive fields in certain limits.

Abstract

We calculate the expectation values of the energy-momentum tensor T_{{\mu}{\nu}} for massive scalar and spinor fields, in the Minkowski-like vacuum states on the two flat spaces which are quotients of Minkowski space under the discrete isometries (t,x,y,z)\mapsto(t,x,y,z+2a) and (t,x,y,z)\mapsto(t,-x,-y,z+a). The results on the first space confirm the literature. The results on the second space are new. We note some qualitative differences between the massless and massive fields in the limits of large a and large x^2+y^2.