Geometric quantization on homogeneous spaces and the meaning of `inequivalent' quantizations

TL;DR

This paper explores geometric quantization on homogeneous spaces, providing a physical interpretation of the multiple inequivalent quantizations that arise, especially in the context of particles in external Yang-Mills fields.

Contribution

It offers a reinterpretation of Mackey-Isham quantization results, clarifying the physical meaning of inequivalent quantizations in geometric quantization.

Findings

Reinterpreted Mackey-Isham quantization results

Provided physical interpretation of inequivalent quantizations

Applied to particles in external Yang-Mills fields

Abstract

Consideration of the geometric quantization of the phase space of a particle in an external Yang-Mills field allows the results of the Mackey-Isham quantization procedure for homogeneous configuration spaces to be reinterpreted. In particular, a clear physical interpretation of the `inequivalent' quantizations occurring in that procedure is given.