Noether's Second Theorem and Ward Identities for Gauge Symmetries

TL;DR

This paper employs Noether's second theorem within the path integral framework to derive and interpret Ward identities associated with large gauge transformations and diffeomorphisms across various gauge theories, revealing new insights.

Contribution

It reintroduces Noether's second theorem in the context of gauge symmetries and demonstrates its utility in generating and understanding Ward identities in gauge theories and gravity.

Findings

Derivation of Ward identities for large gauge transformations

Application to Maxwell, Yang-Mills, p-form, and gravity theories

New physical insights into gauge symmetries and their remnants

Abstract

Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We use Noether's second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether's second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether's second theorem and known results in the recent literature. Our approach suggests a novel point of view with important physical consequences.