Quantum field theory on Clifford-Klein space-times. The effective Lagrangian and vacuum stress-energy tensor

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Abstract
The vacuum-averaged stress-energy tensor is calculated for a scalar field on a variety of static space-times, T(X)M3, where the spatial section, M3, is a Clifford-Klein space form of the flat or spherical type, R3/ Gamma , or S3/ Gamma . The particular examples when M3 is a Klein-bottle waveguide, R(X)K2, or a lens-space, S3/Zm, are treated in most detail. It is found that the vacuum stress on quotient spaces is not of the same tensorial structure as Rmu nu -1/2gmu nu R. This leads to difficulties with the back-reaction problem. It is further found that 'twisting' the field alters the vacuum stress compared to the untwisted theory. Values for the total energies in the three types of polyhedral cellular decompositions of S3 are given. Dirichlet boundary conditions for rectangular cavities are also considered.

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