Topology of Equivalent Unconstrained Systems in QCD

We consider the derivation of equivalent unconstrained systems for QCD given in the class of functions of nontrivial topological gauge transformations. We show that the unconstrained QCD obtained by resolving the Gauss law constraint contains a monopole, a zero mode of the Gauss law, and a rising potential, which can explain the phenomena of confinment and hadronization as well as spontaneous chiral symmetry breaking and the $\eta$-${\eta }^{\mathrm{\prime }}$-mass difference.