A note on the Casimir energy of a massive scalar field in positive curvature space

Abstract

We re-evaluate the zero point Casimir energy for the case of a massive scalar field in ${\mathbf{R}}^1\times {\mathbf{S}}^3$ space, allowing also for deviations from the standard conformal value $\xi =1/6$, by means of zero temperature zeta function techniques. We show that for the problem at hand this approach is equivalent to the high temperature regularization of the vacuum energy, as conjectured in a previous publication. Two different, albeit equally valid, ways of doing the analytic continuation are described.

6 pages, no figures

References in corpus (4)

• Zeta Functions and the Casimir Energy
• Entropy Bounds in $R\times S^3$ Geometries
• The thermal energy of a scalar field in a one-dimensional compact space
• Entropy bounds for massive scalar field in positive curvature space

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