Renormalization Group and DSEs in Non-kinematic Renormalization

The goal of the fourth chapter is to understand which features of renormalized Green functions and the renormalization group change if one uses non-kinematic renormalization conditions. In Sect. 4.1, we generalize our previous constructions, both in the language of Hopf algebras as well as in terms of traditional renormalization group equations, to incorporate arbitrary renormalization schemes. We establish which properties do and which do not change in that case. In particular, we find that the anomalous dimension and the beta function still exist, but the concrete form of these functions depends on the scheme. We introduce the Minimal Subtraction scheme, arguably the most popular non-kinematic renormalization scheme, and discuss its most salient properties.