Local BRST cohomology in gauge theories
type: Item
instance of: scholarly article
title: Local BRST cohomology in gauge theories
zbMATH Open document ID: 1097.81571
DOI: 10.1016/S0370-1573(00)00049-1
author: Marc Henneaux
author: Glenn Barnich
author: Friedemann Brandt
published in: Physics Reports
publication date: 2000-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0002245
review text: The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge-invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non-power counting renormalizable couplings has also been worked out in any number of space-time dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields (``antifields'') included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81T70
zbMATH DE Number: 1519047
Wikidata QID: Q55954649
MaRDI profile type: Publication
arXiv ID: hep-th/0002245
cites work: The geometry of the master equation and topological quantum field theory.
cites work: New spin-one gauge theory in three dimensions
cites work: Novel generalization of three-dimensional Yang–Mills theory
cites work: On the Existence of Global Variational Principles
cites work: Q4036963
cites work: Removal of divergences with the Batalin-Vilkovisky formalism
cites work: More on the subtraction algorithm
cites work: Yang–Mills cohomology in four dimensions
cites work: Nonpolynomial Yang–Mills local cohomology
cites work: Diffeomorphism cohomology in Beltrami parametrization
cites work: Diffeomorphism cohomology in Beltrami parametrization. II. The 1-forms
cites work: Renormalization of gauge invariant operators and anomalies in Yang-Mills theory
cites work: Local BRST cohomology in Einstein-Yang-Mills theory
cites work: Local BRST cohomology in the antifield formalism. I: General theorems
cites work: Local BRST cohomology in the antifield formalism. II: Application to Yang-Mills theory
cites work: Cohomological analysis of gauge-fixed gauge theories
cites work: A generalized canonical formalism and quantization of reducible gauge theories
cites work: An Sp(2)-covariant quantization of gauge theories with linearly dependent generators
cites work: General quantum antibrackets
cites work: OPEN GROUP TRANSFORMATIONS WITHIN THE Sp(2)-FORMALISM
cites work: Algebra of higher antibrackets
cites work: Q3092737
cites work: BRST cohomology for 2D gravity
cites work: Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations
cites work: The anomaly structure of theories with external gravity
cites work: Weyl cocycles
cites work: Q5597608
cites work: The BRST-antibracket cohomology of 2D gravity conformally coupled to scalar matter
cites work: Cohomological analysis of bosonic D-strings and 2d sigma models coupled to abelian gauge fields
cites work: The Batalin, Fradkin, and Vilkovisky formalism for higher-order theories
cites work: Characteristic Cohomology of Differential Systems (I): General Theory
cites work: Becchi–Rouet–Stora cohomology of zero curvature systems. I. The complete ladder case
cites work: Cohomology Theory of Lie Groups and Lie Algebras
cites work: Renormalization
cites work: Non-local conformal anomalies
cites work: On the local Chevalley cohomology of the dynamical Lie algebra of a symplectic manifold
cites work: Quantum Theory of Gravity. II. The Manifestly Covariant Theory
cites work: Q4036974
cites work: Calculation of BRS cohomology with spectral sequences
cites work: Polynomial form of the Stueckelberg model
cites work: B.R.S. algebras. Analysis of the consistency equations in gauge theory
cites work: Q3740709
cites work: Systèmes dynamiques contraints: l'approche homologique. (Constraint dynamical systems: homological approach)
cites work: Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts
cites work: Homological perturbation theory and the algebraic structure of the antifield-antibracket formalism for gauge theories
cites work: Quantization of relativistic systems with constraints
cites work: Hamiltonian formalism, quantization and \(S\) matrix for supergravity
cites work: Antisymmetric tensor gauge theories and nonlinear \(\sigma\)-models
cites work: Noncommutative differential calculus and the axial anomaly in abelian lattice gauge theories
cites work: Q3865176
cites work: Perturbation theory and locality in the field–antifield formalism
cites work: Are nonrenormalizable gauge theories renormalizable?
cites work: Practical algebraic renormalization
cites work: Q4150360
cites work: On the theory and applications of differential torsion products
cites work: On a perturbation theory for the homology of the loop-space
cites work: Q3780116
cites work: Perturbation theory in differential homological algebra. I
cites work: Algebraic aspects of Chen's twisting cochain
cites work: BRST cohomology in classical mechanics
cites work: Spacetime locality of the BRST formalism
cites work: Q4840214

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cites work: Q4251650

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cites work: Characteristic cohomology of \(p\)-form gauge theories

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cites work: BRST cohomology of the Chapline-Manton model

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cites work: The Wess-Zumino consistency condition for \(p\)-form gauge theories

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cites work: Semi-invariant terms for gauged nonlinear \(\sigma\)-models

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cites work: Q5831642

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cites work: Quantum Noether method

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cites work: On the geometry of the Batalin-Vilkovisky formalism

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cites work: Q5731354

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cites work: Homologie et cohomologie des algèbres de Lie

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cites work: Applications of perturbation theory to iterated fibrations

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cites work: Differential vertex operations in Lagrangian field theory

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cites work: Topology and the axial anomaly in abelian lattice gauge theories

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cites work: Algebraic study of chiral anomalities

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cites work: Yang–Mills theory and the Batalin–Fradkin–Vilkovisky formalism

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cites work: Classical Physics as geometry. Gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space

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cites work: Q3803878

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cites work: Q3726964

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cites work: Algebraic Renormalization

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cites work: The supercurrent trace identities of the \(N=1\), \(D=4\) super-Yang-Mills theory in the Wess-Zumino gauge

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cites work: Q3994886

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cites work: The cohomological construction of Stora's solutions

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cites work: Q4036988

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cites work: Infinitesimal computations in topology

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cites work: A global version of the inverse problem of the calculus of variations

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cites work: BRST cohomology in Beltrami parametrization.

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cites work: KOSZUL–TATE COHOMOLOGY FOR AN SP(2)-COVARIANT QUANTIZATION OF GAUGE THEORIES WITH LINEARLY DEPENDENT GENERATORS

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cites work: Natural symmetries of the Yang–Mills equations

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cites work: Q4870992

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cites work: On variation bicomplexes associated to differential equations

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cites work: Q3906145

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cites work: Q4251657

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cites work: Q4188462

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cites work: Q4192712

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cites work: The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. I: The linear theory

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cites work: Q3715834

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cites work: On identically closed forms locally constructed from a field

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cites work: Q4856602

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cites work: Q4343021

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cites work: A note on the antibracket formalism

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cites work: Conservation of Isotopic Spin and Isotopic Gauge Invariance

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cites work: Q3215171

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cites work: Q4453275