On the Emergence of Gauge Structures and Generalized Spin when Quantizing on a Coset Space

McMullan, David and Tsutsui, I. (1993) On the Emergence of Gauge Structures and Generalized Spin when Quantizing on a Coset Space. (Preprint)

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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 Gill. 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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 09 Jul 2018 14:39
Last Modified: 19 Jul 2018 10:06
URI: http://dair.dias.ie/id/eprint/886

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