Quantum Fields in Hyperbolic Space-Times with Finite Spatial Volume

الأصل · EN

The one-loop effective action for a massive self-interacting scalar field is investigated in 4-dimensional ultrastatic space-time R × H³/Γ, H³/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.