Casimir energy density for spherical universes in n-dimensional spacetime

Details Casimir energy density for spherical universes in n-dimensional spacetime Casimir energy density for spherical universes in n-dimensional spacetime

Sep 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cqgra..23.5531o&link_type=abstract

Classical and Quantum Gravity, Volume 23, Issue 18, pp. 5531-5546 (2006).

Physics

Scientific paper

We consider the Casimir effect for the massless conformal scalar field in an n-dimensional, closed, static universe. We calculate the renormalized vacuum energy density using the covariant point-splitting method, the mode-sum regularization and the renormalized vacuum energy with the zeta-function regularization. We observe that all odd spacetime dimensions give us the zero renormalized vacuum energy density. For even spacetime dimensions the renormalized vacuum energy density oscillates in sign. The result agrees with three regularization techniques. The Casimir energy density for spherical universes in n-dimensional spacetime is regarded as interesting both to understand the correspondence between the sign of the effect and the dimension of manifold in topology and as a key to confirming the Casimir energy for half spherical universes (manifold with boundary) in n-dimensional spacetime.

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