Helmholtz Free Energy for Certain Negatively Curved Space-Times, and the Selberg Trace Formula

Abstract

It is very interesting to consider the computation of the quantum statistical quantities F(T), S(T), U(T), for example, of Chapter 14, in a topological setting, given a suitable partition function Z(T), and in particular to understand the dependence of such quantities on the given topology. We are particularly interested in the case when the topology is that of a product ℝ^p × M^d, where M^d is a compact hyperbolic manifold of dimension d ≥ 2, which we conveniently express as (16.1.1)