p-forms on d-spherical tessellations

The spectral properties of p-forms on the fundamental domains of regular tesselations of the d-dimensional sphere are discussed. The degeneracies for all ranks, p, are organised into a double Poincare series which is explicitly determined. In the particular case of coexact forms of rank (d-1)/2, for odd d, it is shown that the heat--kernel expansion terminates with the constant term, which equals (-1)^{p+1}/2 and that the boundary terms also vanish, all as expected. As an example of the double domain construction, it is shown that the degeneracies on the sphere are given by adding the absolute and relative degeneracies on the hemisphere, again as anticipated. The eta invariant on a fundamental domain is computed to be irrational. The spectral counting function is calculated and the accumulated degeneracy give exactly. A generalised Weyl-Polya conjecture for p-forms is suggested and verified.Comment: 23 pages. Section on the counting function adde

The birth of spacetime atoms as the passage of time

The view that the passage of time is physical finds expression in the classical sequential growth models of Rideout and Sorkin in which a discrete spacetime grows by the partially ordered accretion of new spacetime atoms.Comment: Article based on an invited talk at the conference "Do we need a physics of passage?" Cape Town, South Africa, 10-14 Dec 2012. Submitted for publication in Annals of the New York Academy of Sciences (2014

Heat kernels on curved cones

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.Comment: 4p.,sign errors corrected and a small addition,uses JyTeX,MUTP/94/0