Spherical Universe topology and the Casimir effect

TL;DR

This paper investigates the effects of spherical universe topology on the Casimir effect, deriving degeneracies and vacuum energies for massless fields on factored 3-spheres and lens spaces using geometric and spectral methods.

Contribution

It provides a geometric derivation of degeneracies and explicit calculations of vacuum energies and scalar determinants for fields on spherical topologies, including lens spaces.

Findings

Degeneracies on factored 3-spheres and lens spaces are derived geometrically.

Vacuum energies are expressed in terms of polyhedral degrees and cyclic group decompositions.

Explicit forms of spectral asymmetry functions are obtained for lens spaces.

Abstract

The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies are expressed in terms of the polyhedral degrees and equivalent expressions given using the cyclic decomposition of the covering group. Scalar functional determinants are calculated and the spectral asymmetry function treated by the same approach with explicit forms on one-sided lens spaces.