Localization, conformal motions and the duistermaat-heckman theorem

Abstract Here we develop an explicitly covariant expression for the stationary phase approximation of a classical partition function based on geometric properties of the phase space. As an example of the utility of such an evaluation we show that in the case of the Hamiltonian flows generating conformal rescalings of the underlying geometry, the classical partition function is given exactly by the leading term of the stationary phase approximation. We give an explicit example of such an extension of the Duistermaat-Heckman theorem.