Calculation of the Casimir Force between Similar and Dissimilar Metal Plates at Finite Temperature

The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu, or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T=300 K and T=350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.Comment: 23 latex pages, 12 figures. Introductory section expanded, 4 new references. To appear in J. Phys. A: Math. Ge

p-form spectra and Casimir energies on spherical tesselations

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