Gauge Invariance, the Quantum Action Principle, and the Renormalization Group

TL;DR

This paper discusses how gauge invariance can be restored in Wilsonian renormalization group formulations using a cutoff, through an effective Quantum Action Principle that allows solving Ward identities order by order in perturbation theory.

Contribution

It introduces an effective Quantum Action Principle that facilitates solving effective Ward identities in gauge theories with cutoff-dependent RG formulations.

Findings

Gauge invariance is recoverable after removing the cutoff.

The effective Quantum Action Principle enables perturbative solutions of Ward identities.

Challenges with non-perturbative approaches are briefly addressed.

Abstract

If the Wilsonian renormalization group (RG) is formulated with a cutoff that breaks gauge invariance, then gauge invariance may be recovered only once the cutoff is removed and only once a set of effective Ward identities is imposed. We show that an effective Quantum Action Principle can be formulated in perturbation theory which enables the effective Ward identities to be solved order by order, even if the theory requires non-vanishing subtraction points. The difficulties encountered with non-perturbative approximations are briefly discussed.