Absence of $CP$ violation in the strong interactions

Understand

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

• For this purpose, we first build the Green's functions in the one-instanton background and then sum over the configurations of background instantons.
• The quantization of topological sectors follows for saddle points of finite Euclidean action in an infinite spacetime volume and the fluctuations about these.
• For the resulting correlation functions, we therefore take the infinite-volume limit before summing over topological sectors.