Ward identities and Wilson renormalization group for QED

TL;DR

This paper demonstrates that a Wilson renormalization group approach to QED can preserve Ward identities at all perturbative orders, providing a new proof of its renormalizability despite the effective Lagrangian's gauge symmetry breaking.

Contribution

It introduces a formulation of QED with Wilson RG that maintains Ward identities and offers a simplified proof of perturbative renormalizability.

Findings

Renormalized Green's functions satisfy Ward identities at all orders.

The loop expansion is derived from Polchinski's RG equation.

A new simple proof of perturbative renormalizability is provided.

Abstract

We analyze a formulation of QED based on the Wilson renormalization group. Although the ``effective Lagrangian'' used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's functions correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski's renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponding counterterms are generated in the process of fixing the physical conditions.