Inequivalent Quantizations of Gauge Theories

TL;DR

This paper explores the multiple possible quantizations of gauge theories on complex topological spaces, employing a generalized Dirac framework to identify inequivalent quantum sectors distinguished by topological charges.

Contribution

It applies a new generalized Dirac approach to Yang-Mills theory, revealing novel inequivalent quantum sectors labeled by topological charges.

Findings

Identification of inequivalent quantum sectors in Yang-Mills theory

Use of a generalized Dirac framework for quantization

Topological charges label distinct quantum sectors

Abstract

It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for coset spaces. Recently, a new framework for these inequivalent quantizations approach has been proposed by McMullan and Tsutsui, which is based on a generalized Dirac approach. We employ this framework for the quantization of the Yang-Mills theory in the simplest fashion. The resulting inequivalent quantum sectors are labelled by quantized non-dynamical topological charges.