English

p-form spectra and Casimir energies on spherical tesselations

High Energy Physics - Theory 2009-11-11 v3 General Relativity and Quantum Cosmology Mathematical Physics math.MP Spectral Theory

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