The unitary Master Ward Identity: Time slice axiom, Noether's Theorem and Anomalies

TL;DR

This paper introduces a unitary version of the Master Ward Identity within the C*-algebraic framework of quantum field theory, linking it to the time slice axiom, Noether's Theorem, and anomalies, offering new insights and methods.

Contribution

It presents a novel unitary formulation of the Master Ward Identity that enforces the time slice axiom and provides a new approach to Noether's Theorem in quantum field theory.

Findings

The unitary Master Ward Identity implies the time slice axiom.

It enables a direct construction of symmetry implementing unitaries.

It reveals new aspects of anomalies in quantum field theory.

Abstract

The C*-algebraic formulation of generic interacting quantum field theories, recently presented by Detlev Buchholz and one of the authors (KF), is enriched by a unitary version of the Master Ward Identity, which was postulated some time ago by Franz Marc Boas, Ferdinand Brennecke and two of us (MD,KF). It is shown that the corresponding axiom implies the validity of the time slice axiom. Moreover, it opens the way for a new approach to Noether's Theorem where it yields directly the unitaries implementing the symmetries. It also unravels interesting aspects of the role of anomalies in quantum field theory.