The Master Ward Identity

TL;DR

The paper introduces a universal 'master Ward identity' in perturbative quantum field theory that encodes symmetries and is compatible with existing normalization conditions, aiding in the construction of physical observables.

Contribution

It proposes the master Ward identity as a new normalization condition that captures classical symmetries and is compatible with causal perturbation theory, including applications to BRST symmetry.

Findings

The master Ward identity can nearly always be satisfied, except in cases of anomalies.

Compatibility of the master Ward identity with other normalization conditions is proven.

Application to non-Abelian gauge theories yields a master BRST-identity for observable construction.

Abstract

In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, charge- and ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry. It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered. Application of the master Ward identity to the BRST-current of non-Abelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.