Quantum Noether Method

Abstract

We present a general method for constructing consistent quantum field theories with global symmetries. We start from a free non-interacting quantum field theory with given global symmetries and we determine all consistent perturbative quantum deformations assuming the construction is not obstructed by anomalies. The method is established within the causal Bogoliubov-Shirkov-Epstein-Glaser approach to perturbative quantum field theory (which leads directly to a finite perturbative series and does not rely on an intermediary regularization). Our construction can be regarded as a direct implementation of Noether's method at the quantum level. We illustrate the method by constructing the pure Yang-Mills theory (where the relevant global symmetry is BRST symmetry), and the N=1 supersymmetric model of Wess and Zumino. The whole construction is done before the so-called adiabatic limit is taken. Thus, all considerations regarding symmetry, unitarity and anomalies are well-defined even for massless theories.

53 pages, latex, version to appear in Nuclear Physics B

References in corpus (4)

• Self-Interaction and Gauge Invariance
• Polynomial Form of the Stueckelberg Model
• On Gauge Invariance and Spontaneous Symmetry Breaking
• Gauge Independence of the S-Matrix in the Causal Approach

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• Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories
• Eleven dimensional supergravity in light cone gauge
• UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited
• New aspects of the Z${}_{\text{2}}$ $\times$ Z${}_{\text{2}}$-graded 1D superspace: induced strings and 2D relativistic models
• Regularization in quantum field theory from the causal point of view
• The Wess Zumino consistency condition: a paradigm in renormalized perturbation theory
• Comments on the Gauge Fixed BRST Cohomology and the Quantum Noether Method
• The Standard Model and its Generalizations in Epstein-Glaser Approach to Renormalization Theory II: the Fermion Sector and the Axial Anomaly
• Algebraic Approach to the 1/N Expansion in Quantum Field Theory
• Perturbative quantum gauge invariance: Where the ghosts come from