On unconstrained SU(2) gluodynamics with theta angle

The Hamiltonian reduction of classical SU(2) Yang–Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing \(\theta\)-angle. It is shown that for any \(\theta\)-angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained non-local theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different \(\theta\)-angles are canonically equivalent as on the original constrained level.