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Journal ArticleDOI

Local BRST cohomology in gauge theories

01 Nov 2000-Physics Reports (North-Holland)-Vol. 338, Iss: 5, pp 439-569
TL;DR: In this article, the cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin are computed in a self-contained manner, with the sources of the BRST variations of the fields included in the problem.
About: This article is published in Physics Reports.The article was published on 2000-11-01 and is currently open access. It has received 611 citations till now. The article focuses on the topics: BRST quantization & Supersymmetric gauge theory.
Citations
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Journal ArticleDOI
01 Dec 1949-Nature
TL;DR: Wentzel and Jauch as discussed by the authors described the symmetrization of the energy momentum tensor according to the Belinfante Quantum Theory of Fields (BQF).
Abstract: To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

2,935 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT), and the results apply to any consistent unitary quantum theory of gravity with a Kerr solution.
Abstract: Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / \hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi and conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}.

1,011 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that there is a bijective correspondence between equivalence classes of asymptotic reducibility parameters and (n−2)-forms in the context of Lagrangian gauge theories.

744 citations


Cites background or methods from "Local BRST cohomology in gauge theo..."

  • ...The left hand sides of the (Euler-Lagrange) equations of motion of the full and the free theory and their total derivatives, ∂(μ)δL/δφ i and ∂(μ)δL /δφ, have been assumed to satisfy important regularity conditions described for instance in [47, 48] and spelled out in detail in the context of Yang-Mills theories in [5]....

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  • ...Using the cohomology of dH and of δ, one can prove [36, 5]:...

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  • ...The cohomological formulation of Noether’s first theorem and of the relation between reducibility parameters and conserved n − 2 forms via descent equations is reviewed [36, 5]....

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  • ...2 Section 3 The bijective correspondence between equivalence classes of reducibility parameters of gauge symmetries and conserved n− 2 forms [36, 5] is reviewed, independently of BRST cohomological arguments....

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  • ...The cohomology groups H k (δ|dH) can be shown [36, 5] to be isomorphic to the local BRST cohomological groups H(s|dH), where the first superscript denotes...

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Journal ArticleDOI
TL;DR: In this article, the surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus, and they are interpreted as a Pfaff system.
Abstract: Surface charges and their algebra in interacting Lagrangian gauge field theories are constructed out of the underlying linearized theory using techniques from the variational calculus. In the case of exact solutions and symmetries, the surface charges are interpreted as a Pfaff system. Integrability is governed by Frobenius’ theorem and the charges associated with the derived symmetry algebra are shown to vanish. In the asymptotic context, we provide a generalized covariant derivation of the result that the representation of the asymptotic symmetry algebra through charges may be centrally extended. Comparison with Hamiltonian and covariant phase space methods is made. All approaches are shown to agree for exact solutions and symmetries while there are differences in the asymptotic context.

350 citations

References
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Book
01 Jan 1986
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Abstract: 1 Introduction to Lie Groups- 11 Manifolds- Change of Coordinates- Maps Between Manifolds- The Maximal Rank Condition- Submanifolds- Regular Submanifolds- Implicit Submanifolds- Curves and Connectedness- 12 Lie Groups- Lie Subgroups- Local Lie Groups- Local Transformation Groups- Orbits- 13 Vector Fields- Flows- Action on Functions- Differentials- Lie Brackets- Tangent Spaces and Vectors Fields on Submanifolds- Frobenius' Theorem- 14 Lie Algebras- One-Parameter Subgroups- Subalgebras- The Exponential Map- Lie Algebras of Local Lie Groups- Structure Constants- Commutator Tables- Infinitesimal Group Actions- 15 Differential Forms- Pull-Back and Change of Coordinates- Interior Products- The Differential- The de Rham Complex- Lie Derivatives- Homotopy Operators- Integration and Stokes' Theorem- Notes- Exercises- 2 Symmetry Groups of Differential Equations- 21 Symmetries of Algebraic Equations- Invariant Subsets- Invariant Functions- Infinitesimal Invariance- Local Invariance- Invariants and Functional Dependence- Methods for Constructing Invariants- 22 Groups and Differential Equations- 23 Prolongation- Systems of Differential Equations- Prolongation of Group Actions- Invariance of Differential Equations- Prolongation of Vector Fields- Infinitesimal Invariance- The Prolongation Formula- Total Derivatives- The General Prolongation Formula- Properties of Prolonged Vector Fields- Characteristics of Symmetries- 24 Calculation of Symmetry Groups- 25 Integration of Ordinary Differential Equations- First Order Equations- Higher Order Equations- Differential Invariants- Multi-parameter Symmetry Groups- Solvable Groups- Systems of Ordinary Differential Equations- 26 Nondegeneracy Conditions for Differential Equations- Local Solvability- In variance Criteria- The Cauchy-Kovalevskaya Theorem- Characteristics- Normal Systems- Prolongation of Differential Equations- Notes- Exercises- 3 Group-Invariant Solutions- 31 Construction of Group-Invariant Solutions- 32 Examples of Group-Invariant Solutions- 33 Classification of Group-Invariant Solutions- The Adjoint Representation- Classification of Subgroups and Subalgebras- Classification of Group-Invariant Solutions- 34 Quotient Manifolds- Dimensional Analysis- 35 Group-Invariant Prolongations and Reduction- Extended Jet Bundles- Differential Equations- Group Actions- The Invariant Jet Space- Connection with the Quotient Manifold- The Reduced Equation- Local Coordinates- Notes- Exercises- 4 Symmetry Groups and Conservation Laws- 41 The Calculus of Variations- The Variational Derivative- Null Lagrangians and Divergences- Invariance of the Euler Operator- 42 Variational Symmetries- Infinitesimal Criterion of Invariance- Symmetries of the Euler-Lagrange Equations- Reduction of Order- 43 Conservation Laws- Trivial Conservation Laws- Characteristics of Conservation Laws- 44 Noether's Theorem- Divergence Symmetries- Notes- Exercises- 5 Generalized Symmetries- 51 Generalized Symmetries of Differential Equations- Differential Functions- Generalized Vector Fields- Evolutionary Vector Fields- Equivalence and Trivial Symmetries- Computation of Generalized Symmetries- Group Transformations- Symmetries and Prolongations- The Lie Bracket- Evolution Equations- 52 Recursion Operators, Master Symmetries and Formal Symmetries- Frechet Derivatives- Lie Derivatives of Differential Operators- Criteria for Recursion Operators- The Korteweg-de Vries Equation- Master Symmetries- Pseudo-differential Operators- Formal Symmetries- 53 Generalized Symmetries and Conservation Laws- Adjoints of Differential Operators- Characteristics of Conservation Laws- Variational Symmetries- Group Transformations- Noether's Theorem- Self-adjoint Linear Systems- Action of Symmetries on Conservation Laws- Abnormal Systems and Noether's Second Theorem- Formal Symmetries and Conservation Laws- 54 The Variational Complex- The D-Complex- Vertical Forms- Total Derivatives of Vertical Forms- Functionals and Functional Forms- The Variational Differential- Higher Euler Operators- The Total Homotopy Operator- Notes- Exercises- 6 Finite-Dimensional Hamiltonian Systems- 61 Poisson Brackets- Hamiltonian Vector Fields- The Structure Functions- The Lie-Poisson Structure- 62 Symplectic Structures and Foliations- The Correspondence Between One-Forms and Vector Fields- Rank of a Poisson Structure- Symplectic Manifolds- Maps Between Poisson Manifolds- Poisson Submanifolds- Darboux' Theorem- The Co-adjoint Representation- 63 Symmetries, First Integrals and Reduction of Order- First Integrals- Hamiltonian Symmetry Groups- Reduction of Order in Hamiltonian Systems- Reduction Using Multi-parameter Groups- Hamiltonian Transformation Groups- The Momentum Map- Notes- Exercises- 7 Hamiltonian Methods for Evolution Equations- 71 Poisson Brackets- The Jacobi Identity- Functional Multi-vectors- 72 Symmetries and Conservation Laws- Distinguished Functionals- Lie Brackets- Conservation Laws- 73 Bi-Hamiltonian Systems- Recursion Operators- Notes- Exercises- References- Symbol Index- Author Index

8,118 citations


Additional excerpts

  • ...Useful references on jet-spaces are [178, 186, 6]....

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Book
01 Jan 1963

7,658 citations

MonographDOI
30 Jun 1995
TL;DR: Weinberg as discussed by the authors presented a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics, including supersymmetric algebras.
Abstract: In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, non-perturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, including previously unpublished results. Exercises are included.

4,988 citations

Book
15 Aug 2002
TL;DR: In this paper, a renormalization group analysis is proposed to model the scaling behavior of a field theory in the large N limit of the ferromagnetic order at low temperature.
Abstract: Algebraic preliminaries Euclidean path integrals in quantum mechanics Path integrals in quantum mechanics - generalizations stochastic differential equations - Langevin, Fokker-Planck equations functional integrals in field theory generating functionals of correlation functions - loopwise expansion divergences in pertubation theory, power counting regularization methods introduction to renormalization theory - renormalization group equations dimensional regularization and minimal subtraction - calculation of RG functions renormalization of composite operators - short distance expansion linearly realized symmetries and renormalization non linearly realized symmetries - the examples of the non linear sigma-model models on homogeneous spaces in two dimensions tensorial analysis on Riemannian manifolds symmetric spaces - non local conservation laws, renormalization group Slavnov-Taylor and BRS symmetry - stochastic field equations renormalization and stochastic field equations - supersymmtery Abelian gauge theories non-Abelian gauge theories the standard model - anomalies renormalization of gauge theories - general formalism critical phenomena - general considerations mean field theory for ferromagnetic systems general renormalization group analysis - the critical theory near dimension four scaling behaviour in the critical domain corrections to scaling behaviour calculation of universal quantities the (phi squared) squared field theory in the large N limit ferromagnetic order at low temperature - the non linear sigma-model a few two-dimensional models - bosonization technique the 0 (2) non linear sigma-model critical properties of gauge theories large momentum behaviour in field theory critical dynamics field theory in a finite geometry - finite size scaling instantons in quantum mechanics - the anharmonic oscillator quantum mechanics - generalization unstable vacua in field theory degenerate classical minima and instantons perturbation theory at large orders and instantons - the summation problem the "phi to the fourth" field theory in dimension four fermions and large order behaviour multi-instantons in quantum mechanics

4,335 citations


"Local BRST cohomology in gauge theo..." refers background or methods in this paper

  • ...Thus, while the original point of view on the antifields (sources coupled to the BRST variations of the fields [45, 46, 47, 231, 232]) is useful for the purposes of renormalization theory, the complementary interpretation in terms of equations of...

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  • ...They have been introduced in order to control how the BRST symmetry gets renormalized [45, 46, 47, 231, 232]....

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Journal ArticleDOI
TL;DR: In this article, a new regularization and renormalization procedure for gauge theories is presented, which is particularly well suited for the treatment of gauge theories and is transparent when anomalies such as the Bell-Jackiw-Adler anomaly may occur.

3,722 citations


"Local BRST cohomology in gauge theo..." refers background in this paper

  • ...Yang-Mills theory in four dimensions is power-counting renormalizable [145, 146, 147, 148]....

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  • ...One of the aims was to relate the Slavnov-Taylor identities [188, 200] underlying the proof of power-counting renormalizability [145, 146, 147, 148, 168, 169, 170, 171] to an invariance of the gauge-fixed action (for a recent historical account, see [233])....

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