Renormalization group in the internal space

TL;DR

This paper develops a functional renormalization group approach in the internal space, deriving evolution equations for effective actions in scalar models, including a generalized Callan-Symanzik equation, emphasizing cutoff independence.

Contribution

It introduces a novel functional framework for the renormalization group in internal space, deriving equations for effective actions with cutoff-independent formulations.

Findings

Derived a functional generalization of the Callan-Symanzik equation.

Established evolution equations for two-particle irreducible effective action.

Presented a cutoff-independent formulation of the renormalization group in internal space.

Abstract

Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar model. The evolution in the mass which yields the functional generalization of the Callan-Symanzik equation for the one-particle irreducible effective action is given in its renormalized, cutoff-independent form. The evolution of the coupling constant generates an evolution equation for the two-particle irreducible effective action.