Circle actions and geometric quantisation

Abstract

The aim of this article is to present unifying proofs for results in geometric quantisation with real polarisations by exploring the existence of symplectic circle actions. It provides an extension of Rawnsley's results on the Kostant complex, and gives an alternative proof for Sniatycki's and Hamilton's theorems; as well as, a partial result for the focus-focus contribution to geometric quantisation.Comment: 28 pages; issues concerning flat hermitian line bundles were addressed, results unchange