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Inequivalent Quantizations of Gauge Theories

Kenichi Horie
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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.

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Kenichi Horie. 1999-05-14. Inequivalent Quantizations of Gauge Theories. https://doi.org/10.1142/s0217751x99001020

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