On the emergence of gauge structures and generalized spin when quantizing on a coset space

TL;DR

This paper explores how different quantizations on coset spaces lead to gauge structures and generalized spin, using a modified Dirac approach that allows classical constraints to become anomalous upon quantization.

Contribution

It introduces a novel quantization method for systems on coset spaces that results in gauge fields and spin degrees of freedom, expanding understanding of quantization ambiguities.

Findings

Quantization on coset spaces can produce gauge connections with quantized couplings.

Emergence of spin degrees of freedom in path-integral formalism.

Application to S^4 shows chiral spin coupled to instantons.

Abstract

It has been known for some time that there are many inequivalent quantizations possible when the configuration space of a system is a coset space G/H. Viewing this classical system as a constrained system on the group G, we show that these inequivalent quantizations can be recovered from a generalization of Dirac's approach to the quantization of such a constrained system within which the classical first class constraints (generating the H-action on G) are allowed to become anomalous (second class) when quantizing. The resulting quantum theories are characterized by the emergence of a Yang-Mills connection, with quantized couplings, and new 'spin' degrees of {}freedom. Various applications of this procedure are presented in detail: including a new account of how spin can be described within a path-integral formalism, and how on S^4 chiral spin degrees of {}freedom emerge, coupled to a BPST instanton.