Inequivalent quantizations of gauge theories

It is known that the quantization of a system defined on a topologically nontrivial 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 to the quantization of the Yang-Mills theory in the simplest fashion. The resulting inequivalent quantum systems are labelled by quantized nondynamical topological charges.