Gauge invariant composite operators of QED in the exact renormalization group formalism

TL;DR

This paper uses the exact renormalization group formalism to analyze gauge invariant composite operators in QED, demonstrating gauge fixing parameter independence and providing a proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly.

Contribution

It introduces a method to construct gauge invariant composite operators in QED that are independent of gauge fixing parameters within the ERG formalism.

Findings

Gauge invariant composite operators can be made gauge fixing parameter independent.

A concise proof of the Adler-Bardeen non-renormalization theorem is provided in arbitrary covariant gauges.

The dependence of operators and actions on gauge fixing parameters is systematically analyzed.

Abstract

Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ``gauge fixing parameter independence,'' we show that any gauge independent composite operators can be made ``gauge fixing parameter independent'' by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A. Zee.