Spherical Universe topology and the Casimir effect

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.

33 pages, 1 figure. Typos corrected and one reference added

References in corpus (7)

• Cosmic Topology
• Eigenmodes of 3-dimensional spherical spaces and their application to cosmology
• Vacuum energy on orbifold factors of spheres
• Effective action in spherical domains
• Determinants of Laplacians, the Ray-Singer Torsion on Lens Spaces and the Riemann zeta function
• Zero modes, entropy bounds and partition functions
• Magnetic fields and factored two-spheres

Cited by in corpus (10)

• Tensor model and dynamical generation of commutative nonassociative fuzzy spaces
• Inflation, Large Branes, and the Shape of Space
• The spectral action and cosmic topology
• Functional Determinant of the Massive Laplace Operator and the Multiplicative Anomaly
• Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds
• p-form spectra and Casimir energies on spherical tesselations
• Lens space determinants
• Topological Entropy and Renormalization Group flow in 3-dimensional spherical spaces
• p-forms on d-spherical tessellations
• Aspects of Higher-Abelian Gauge Theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops