  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.
