Hard-Soft Renormalization and the Exact Renormalization Group

TL;DR

This paper develops a framework using the Wilsonian exact renormalization group to handle divergences in massless QED, ensuring infrared finiteness of gauge-invariant operators and their anomalies through flow equations.

Contribution

It introduces a novel renormalization approach that separates UV and IR divergences and proves infrared convergence under specific conditions in massless QED.

Findings

Infrared finiteness of gauge-invariant operators established

Renormalization conditions compatible with Ward identities proven

Application to axial current and anomaly demonstrated

Abstract

The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale $\L_R > 0$. We prove, using the flow equation technique, that infrared convergence is a necessary consequence of any zero-momentum renormalization condition at $\L_R$ compatible with the effective Ward identities and axial symmetry. The same formalism is applied to renormalize gauge-invariant composite operators and to prove their infrared finiteness; in particular we consider the case of the axial current operator and its anomaly.