Products of Current Operators in the Exact Renormalization Group Formalism

TL;DR

This paper develops a method to construct products of current operators within the exact renormalization group framework, ensuring consistency with Ward-Takahashi identities and finite cutoffs, exemplified by chiral fermions.

Contribution

It introduces a systematic way to handle current operator products in Wilson actions using the exact renormalization group, maintaining symmetry identities.

Findings

Successfully constructs current operator products at the Gaussian fixed point

Ensures compatibility of Ward-Takahashi identities with finite momentum cutoffs

Provides a concrete example with chiral fermions

Abstract

Given a Wilson action invariant under global chiral transformations, we can construct current composite operators in terms of the Wilson action. The short distance singularities in the multiple products of the current operators are taken care of by the exact renormalization group. The Ward-Takahashi identity is compatible with the finite momentum cutoff of the Wilson action. The exact renormalization group and the Ward-Takahashi identity together determine the products. As a concrete example, we study the Gaussian fixed-point Wilson action of the chiral fermions to construct the products of current operators.