The Master Ward Identity

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.

73 pages, version to appear in Rev. Math. Phys

References in corpus (3)

• Algebraic Quantum Field Theory, Perturbation Theory, and the Loop Expansion
• Massive Vector Mesons and Gauge Theory
• The Action Principle in Epstein Glaser Renormalization and Renormalization of the S-Matrix in ${\varphi }^4$-Theory

Cited by in corpus (27)

• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Renormalized Quantum Yang-Mills Fields in Curved Spacetime
• Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity
• The Energy-Momentum Tensor(s) in Classical Gauge Theories
• The Master Ward Identity and Generalized Schwinger-Dyson Equation in Classical Field Theory
• Renormalization as a functor on bialgebras
• Removal of violations of the Master Ward Identity in perturbative QFT
• Quantum gauge models without classical Higgs mechanism
• Comments on Microcausality, Chaos, and Gravitational Observables
• All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory
• Renormalized Perturbation Theory: A Missing Chapter
• Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories
• Quantum field theory meets Hopf algebra
• The Wess Zumino consistency condition: a paradigm in renormalized perturbation theory
• Regularization in quantum field theory from the causal point of view
• Proof of perturbative gauge invariance for tree diagrams to all orders
• Perturbative Gravity in the Causal Approach
• A Lorentzian renormalisation group equation for gauge theories
• The Quantum Action Principle in the framework of Causal Perturbation Theory
• Relating on-shell and off-shell formalism in perturbative quantum field theory
• A Generalization of Gauge Invariance
• The Master Ward Identity for scalar QED
• The full electroweak interaction: an autonomous account
• Massive vector bosons: is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?
• The Interaction of Quantum Gravity with Matter
• Perturbative quantum gauge invariance: Where the ghosts come from
• Dressed fields for Quantum Chromodynamics