We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato-Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator...

A non-perturbative solution to strong CP problem is proposed. It is shown that the gauge orbit space with gauge potentials and gauge tranformations restricted on the space boundary in non-abelian gauge theories with a θ term has a magnetic monopole structure if there is a magnetic monopole in the ordinary space. The Dirac’s quantization condition in the corresponding quantum theories ensures th...