Removal of violations of the Master Ward Identity in perturbative QFT

TL;DR

This paper investigates anomalies in the Master Ward Identity within perturbative quantum field theory, demonstrating that violations can be characterized as local interacting fields and can be eliminated through finite renormalizations.

Contribution

It introduces a method to express violations of the Master Ward Identity as local fields and provides a systematic way to remove anomalies via algebraic renormalization techniques.

Findings

Violations of the Master Ward Identity are local interacting fields.

Anomalies can be eliminated by finite renormalizations.

Applied method to prove Ward identities in the O(N) scalar model.

Abstract

We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a LOCAL interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in $\hbar$, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example the method is applied to prove the Ward identities of the O(N) scalar field model.