Vacuum energy on orbifold factors of spheres

Abstract

The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \R$\times {\S }^2/\Gamma$ where $\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\Gamma$ is composed of pure rotations but not otherwise. It is shown on general grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Bernoulli functions (i.e. Todd polynomials). The relevant $\zeta$- functions are analysed in some detail and several identities are incidentally derived. The general discussion is presented in terms of finite reflection groups.

29 pages, latex

References in corpus (1)

• Vacuum energies on spheres and in cubes

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