The Ward Identity from the Background Field Dependence of the Effective Action

TL;DR

This paper explores how the background field dependence of the effective action in gauge theories leads to Ward identities, highlighting their derivation for Abelian theories and implications for infrared cutoff methods.

Contribution

It demonstrates that the Ward identity can be derived from the background field identity in Abelian gauge theories, clarifying their relationship and relevance for flow equations.

Findings

Ward identity follows from background field identity in Abelian theories

Relevance for gauge theories with infrared cutoff

Implications for flow equation methods

Abstract

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We argue that for Abelian theories the Ward identity follows from the more general background field identity. This observation is particularly relevant for the anomalous Ward identity valid for gauge theories with an effective infrared cutoff as used for flow equations.