Manifestly gauge invariant exact renormalization group for quantum electrodynamics

TL;DR

This paper develops a gauge-invariant formulation of the exact renormalization group for quantum electrodynamics using gauge covariant diffusion equations, deriving key quantum corrections and maintaining gauge symmetry.

Contribution

It introduces a gauge-invariant GFERG framework for QED and computes the 1-loop beta function and anomalous dimensions while preserving gauge Ward identities.

Findings

Derived the 1-loop beta function for QED.

Calculated anomalous dimensions consistent with gauge invariance.

Maintained gauge Ward--Takahashi identities in the Wilson action.

Abstract

We formulate quantum electrodynamics on the basis of gauge (or BRST) covariant diffusion equations of fields. This is a particular example of the gradient flow exact renormalization group (GFERG). The resulting Wilson action fulfills a simple gauge Ward--Takahashi identity. We solve the GFERG equation around the Gaussian fixed point to the second order in gauge coupling and obtain the 1-loop beta function and anomalous dimensions. The anomalous dimension of the electron field coincides with that of the fermion field diffused by a gauge covariant flow equation of L\"uscher.