TL;DR
This paper explores the role of symplectic circle actions in geometric quantisation, providing unified proofs and extending existing results related to real polarisations and the Kostant complex.
Contribution
It offers unifying proofs for key theorems in geometric quantisation using symplectic circle actions and extends prior results by Rawnsley, Sniatycki, and Hamilton.
Findings
Extended Rawnsley's results on the Kostant complex
Provided an alternative proof for Sniatycki's and Hamilton's theorems
Presented a partial result for focus-focus contributions
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.
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