Equivariant Localization and Stationary Phase

Abstract

Equivariant cohomology in general and the equivariant localization theorems in particular have taken on a role of increasing significance in theoretical physics of late (see e.g. [3], [4] and [10]). These lectures are an attempt to provide a self-contained and elementary introduction to the Cartan model of equivariant cohomology, a complete proof of the simplest of the localization theorems, and, as an application, a proof of the famous Duistermaat–Heckman theorem on exact stationary phase approximations.