  We show that the class of functions of topologically nontrivial gauge
transformations in QCD includes a zero-mode of the Gauss law constraint. The
equivalent unconstrained system compatible with Feynman's integral is derived
in terms of topological invariant variables, where the zero-mode is identified
with the winding number collective variable and leads to the dominance of the
Wu-Yang monopole. Physical consequences of Feynman's path integral in terms of
the topological invariant variables are studied.
