On the construction of QED using ERG

TL;DR

This paper demonstrates how to construct Quantum Electrodynamics (QED) using the exact renormalization group (ERG), ensuring gauge invariance through Ward identities and BRST symmetry, with a focus on the role of momentum cutoffs.

Contribution

It provides a concrete method to build QED with ERG, including a new derivation of Ward identities and their realization as BRST invariance.

Findings

Ward identity derived via composite operators

Parameters fine-tuned for gauge invariance

Wilson action invariant under BRST transformation

Abstract

It has been known for some time that a smooth momentum cutoff is compatible with local gauge symmetries. In this paper we show concretely how to construct QED using the exact renormalization group (ERG). First, we give a new derivation of the Ward identity for the Wilson action using the technique of composite operators. Second, parameterizing the theory by its asymptotic behavior for a large cutoff, we show how to fine-tune the parameters to satisfy the identity. Third, we recast the identity as invariance of the Wilson action under a non-linear BRST transformation.