correlation functions for massive fermions with a complex mass in the presence of a general vacuum angle

Absence of $CP$ violation in the strong interactions

Correlation functions for massive fermions with a complex mass are derived in the presence of a general vacuum angle.The quantization of topological sectors follows for saddle points of finite euclidean action in an infinite-spacetime volume and the fluctuations about these.In contrast to the opposite order of limits, the chiral phases from the mass terms and from the instanton effects then are aligned so that, in absence of additional phases, these do not give rise to observables violating charge-parity symmetry.