Prof. Björn Garbrecht

In this seminar, I will review the topological aspects of SU(2) Yang--Mills theory (as a subgroup of the QCD gauge symmetry) as well as the CP-odd rephasing invariant of the Lagrangian with quark masses and a topological term. It is commonly thought that the rephasing invariant leads to a neutron electric dipole moment as a CP-odd observable. However, I will then explain, in contrast to the conventional point of view, why the strong interactions conserve CP no matter the value of the CP-odd invariant. This conclusion can be reached in two independent ways:

1. Topological quantization in the Euclidean path integral is a consequence of infinite spacetime volume. Therefore, the spacetime volume must be taken to infinity before summing over topological sectors. This order also follows from a construction of the Cauchy contour for the path integral via steepest descent methods. We then find CP conservation. Changing the order of limits corresponds to an illicit, singular deformation of the contour and to the standard conclusion of CP violation.

2. In canonical quantization, relevant e.g. for lattice gauge theory, it is usually assumed that in addition to the temporal gauge condition the allowed gauge transformations go to a constant on the boundary of the spatial hypersurface on which the state lives. This extra constraint is however not taken into account in the commutation relations. We hence drop it and show that the wave functional is invariant under generalized gauge transformations. This again leads us to conclude CP conservation and resolves an unsettling issue with the standard approach, where the vacuum state is not properly normalizable, in conflict with one of the axioms of quantum mechanics.