Chiral symmetry breaking and θ vacuum structure in QCD

The solution of the axial U(1) problem, the role of the topology of the gauge group in forcing the breaking of axial symmetry in any irreducible representation of the observable algebra and the θ vacua structure are revisited in the temporal gauge with attention to the mathematical consistency of the derivations. Both realizations with strong and weak Gauss law are discussed; the control of the general mechanisms and structures is obtained on the basis of the localization of the (large) gauge transformations and the local generation of the chiral symmetry. The Schwinger model in the temporal gauge exactly reproduces the general results.