1992/10/02 by Peter Chang, J. S. Dowker · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Quantum Electrodynamics and Casimir Effect #hep-th
paper · pdf · doi:10.1016/0550-3213(93)90223-c
published as Nucl.Phys.B395:407-432,1993 · 29 pages, latex
arxiv created 1992/10/02 · openalex publication_date 1993/04/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \R× §2/Γ where Γ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when Γ 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 ζ- functions are analysed in some detail and several identities are incidentally derived. The general discussion is presented in terms of finite reflection groups.