Inequivalent Quantizations of Gauge Theories

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.

24 pages, LaTeX, to be publ. in Int.J.Mod.Phys. A

References in corpus (2)

• BPST instanton and Spin from inequivalent quantizations
• Geometric Quantization of the Phase Space of a Particle in a Yang-Mills Field