Geometric quantisation of the global Liouville mechanics

TL;DR

This paper applies geometric quantization to the reduced SL(2,R) WZW quantum mechanics, determining its spectrum and establishing a unique, physically preferred quantization method.

Contribution

It introduces a geometric quantization framework for the SL(2,R) WZW quantum mechanics, resolving ambiguities in previous approaches.

Findings

Spectrum of the Hamiltonian is explicitly determined.

A unique, physically preferred quantization is identified.

Contrasts with previous methods that lacked a definitive quantization choice.

Abstract

The reduced SL(2,R) WZW quantum mechanics is analysed in the framework of geometric quantization. The spectrum of the Hamiltonian is determined, and it is found, that contrary to the previous approaches, there is a unique, physically preferred quantisation of the system.