The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory

TL;DR

This paper explores the Master Ward Identity in classical field theory, revealing it as the most general identity derived from field equations, and links it to the generalized Schwinger-Dyson Equation and the Quantum Action Principle.

Contribution

It provides a classical interpretation of the Master Ward Identity, showing its equivalence to a generalized Schwinger-Dyson Equation and connecting it to foundational principles in quantum field theory.

Findings

Master Ward Identity is the most general identity from field equations.

It is equivalent to a generalized Schwinger-Dyson Equation.

Provides a covariant Poisson bracket formulation.

Abstract

In the framework of perturbative quantum field theory a new, universal renormalization condition (called Master Ward Identity) was recently proposed by one of us (M.D.) in a joint paper with F.-M. Boas. The main aim of the present paper is to get a better understanding of the Master Ward Identity by analyzing its meaning in classical field theory. It turns out that it is the most general identity for classical local fields which follows from the field equations. It is equivalent to a generalization of the Schwinger-Dyson Equation and is closely related to the Quantum Action Principle of Lowenstein and Lam. As a byproduct we give a self-contained treatment of Peierls' manifestly covariant definition of the Poisson bracket.