Functional Callan-Symanzik equation

TL;DR

This paper introduces a functional approach to derive exact evolution equations for the effective action, generalizing Callan-Symanzik equations and connecting with Wilsonian renormalization group flows.

Contribution

It presents a novel functional method to obtain exact evolution equations, unifying different parameters like mass and Planck constant within a common framework.

Findings

Derivation of a functional generalization of Callan-Symanzik equations.

Establishment of the connection between these equations and Wilsonian renormalization flows.

Recovery of the standard one-loop effective action.

Abstract

We describe a functional method to obtain the exact evolution equation of the effective action with a parameter of the bare theory. When this parameter happens to be the bare mass of the scalar field, we find a functional generalization of the Callan-Symanzik equations. Another possibility is when this parameter is the Planck constant and controls the amplitude of the fluctuations. We show the similarity of these equations with the Wilsonian renormalization group flows and also recover the usual one loop effective action.