Vacuum energies on spheres and in cubes
J.S.Dowker
TL;DR
This paper calculates the vacuum energy of a conformally coupled scalar field on spheres, tori, and cubes, revealing that it is zero on even spheres, oscillates on odd spheres, and providing results for other geometries.
Contribution
It provides explicit calculations of vacuum energies on various geometries, highlighting differences between even and odd spheres and including tori and cubes.
Findings
Vacuum energy is zero on even-dimensional spheres.
Vacuum energy oscillates in sign on odd-dimensional spheres.
Results for vacuum energies on tori and cubes are also presented.
Abstract
The vacuum energy of a conformally coupled scalar field on the d-dimensional sphere is calculated. On even spheres it is zero and on odd spheres it oscillates in sign. Results for the d-torus and d-cube are also given.
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Taxonomy
TopicsRelativity and Gravitational Theory · Cosmology and Gravitation Theories · Algebraic and Geometric Analysis