Products of composite operators in the exact renormalization group formalism

TL;DR

This paper presents a method for constructing products of composite operators within the exact renormalization group framework, enabling the calculation of short distance expansions and their coefficients through differential equations.

Contribution

It introduces a novel approach to compute operator product expansions using the exact renormalization group formalism at fixed points.

Findings

Validated the method with simple examples

Derived differential equations for expansion coefficients

Confirmed the validity of short distance expansions

Abstract

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.