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

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.