Exact Renormalization Group : A New Method for Blocking the Action

TL;DR

This paper introduces a new exact renormalization group method for non-canonical scalar field theories, establishing relations between different formulations and illustrating potential applications in liquid theory.

Contribution

It presents a novel approach to the exact renormalization group for non-canonical fields, including a mapping between canonical and non-canonical theories and their flow relations.

Findings

Relation between Wilsonian and effective actions via Legendre transform

Exact mapping between canonical and non-canonical theories

Application outline for liquid theory

Abstract

We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the relations between their flows. An application to the theory of liquids is sketched.