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.
Keywords
Cite
@article{arxiv.hep-th/0510248,
title = {p-form spectra and Casimir energies on spherical tesselations},
author = {J. S. Dowker},
journal= {arXiv preprint arXiv:hep-th/0510248},
year = {2009}
}
Comments
43 pages. v.ii. Puzzle eliminated, references added and typos corrected. v.iii. topological arguments included, references added