p-form spectra and Casimir energies on spherical tesselations

Abstract

Casimir energies on space-times having the fundamental domains of semi-regular spherical tesselations of the three-sphere as their spatial sections are computed for scalar and Maxwell fields. The spectral theory of p-forms on the fundamental domains is also developed and degeneracy generating functions computed. Absolute and relative boundary conditions are encountered naturally. Some aspects of the heat-kernel expansion are explored. The expansion is shown to terminate with the constant term which is computed to be 1/2 on all tesselations for a coexact 1-form and shown to be so by topological arguments. Some practical points concerning generalised Bernoulli numbers are given.

43 pages. v.ii. Puzzle eliminated, references added and typos corrected. v.iii. topological arguments included, references added

References in corpus (3)

• Spherical Universe topology and the Casimir effect
• Spherical Casimir energies and Dedekind sums
• Determinants on lens spaces and cyclotomic units

Cited by in corpus (5)

• Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
• p-forms on d-spherical tessellations
• De Sitter Horizon Edge Partition Functions
• Entropy Bound for the TM Electromagnetic Field in the Half Einstein Universe
• Aspects of Higher-Abelian Gauge Theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops