p-form spectra and Casimir energies on spherical tesselations

Details p-form spectra and Casimir energies on spherical tesselations p-form spectra and Casimir energies on spherical tesselations

2005-10-28

arxiv.org/abs/hep-th/0510248v3

Class.Quant.Grav.23:2771-2802,2006

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0264-9381/23/9/002

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.

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