"Theory of Particle Physics and Cosmology" Seminar

We examine possible effects of the topological term in the QCD-Lagrangian. For the path integral in zero-temperature Euclidean space, topological quantization only emerges in the infinite-volume limit, so that it must be taken prior to summing over winding numbers. This procedure is consistent with the construction of the path-integral contour from steepest-descent flows. As a result, CP violation is absent from observables, in contrast to calculations that rely on singular deformations leading to an inequivalent integration contour with the opposite order of limits. We also address theta-vacua in temporal gauge, which in the conventional picture are not properly normalizable, in contradiction with the axioms of quantum mechanics. However, we show that the possible wave-functionals, given the canonical commutation relations and without introducing extra gauge constraints, are properly normalizable states that do not exhibit CP violation.