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arXiv · hep-th/9605209

Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume

A. A. Bytsenko·Guido Cognola·Sergio Zerbini
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Abstract

The one-loop effective action for a massive self-interacting scalar field is investigated in $4$-dimensional ultrastatic space-time $ R \times H^3/Γ$, $H^3/Γ$ being a non-compact hyperbolic manifold with finite volume. Making use of the Selberg trace formula, the $ζ$-function related to the small disturbance operator is constructed. For an arbitrary gravitational coupling, it is found that $ζ(s)$ has a simple pole at $s=0$. The one-loop effective action is analysed by means of proper-time regularisations and the one-loop divergences are explicitly found. It is pointed out that, in this special case, also $ζ$-function regularisation requires a divergent counterterm, which however is not necessary in the free massless conformal invariant coupling case. Finite temperature effects are studied and the high-temperature expansion is presented. A possible application to the problem of the divergences of the entanglement entropy for a free massless scalar field in a Rindler-like space-time is briefly discussed.

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A. A. Bytsenko, Guido Cognola, Sergio Zerbini. 1996-10-23. Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume. https://doi.org/10.1088/0264-9381%2F14%2F3%2F008

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