The propagator for quantum mechanics on a group manifold from an infinite-dimensional analogue of the Duistermaat-Heckman integration formula

An exact expression for the quantum mechanical propagator for a particle moving on a group manifold is shown to arise from the application of an infinite-dimensional version of the Duistermaat-Heckman integration formula to a suitable path integral over the based loop group of the group. In an appendix the equivalence of this expression to a spectral representation of the propagator is demonstrated by means of a Poisson resummation.