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Journal Article•DOI•

Ghost-creating gauges in Yang-Mills theory

Jean Thierry-Mieg1, Jean Thierry-Mieg2•
University of California, Berkeley1, Centre national de la recherche scientifique2
01 Jan 1985-Nuclear Physics (North-Holland)-Vol. 261, Iss: 1, pp 55-65
TL;DR: In this paper, the authors study the ghost-antighost symmetry of the extended BRS equations, discuss the geometrical interpretation of the formalism and define a new class of gauges in which the ghost number is only conserved modulo two.
About: This article is published in Nuclear Physics.The article was published on 1985-01-01 and is currently open access. It has received 16 citations till now. The article focuses on the topics: BRST quantization & Introduction to gauge theory.

Summary (1 min read)

Jump to: [5. CURCI FERRARI GAUGES] and [CONCLUSION]

5. CURCI FERRARI GAUGES

  • In their formalism, the authors may understand the breaking of unitarity algebraically.
  • In the usual construction, the physical states are defined as cohomology classes of the BRS operator:.
  • It follows that the BRS operator can no longer be used to remove the longitudinal degrees of freedom and the formalism collapses.

CONCLUSION

  • The new gauges considered in this note provide a systematic generalization of several earlier studies [2, 7, 10, 21] .
  • Then, abandoning ghost conservation, the authors have constructed a Feynman gauge where ghost and antighosts pairs are emitted by longitudinal photons, the Sp(2) symmetry is explicit and the 4-ghost interaction is absent.
  • The ghost creating gauges, and the relation to the geometry of the Lie groups, are certainly amusing and curious.

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Citations
More filters
Renormalization of the Abelian Higgs-Kibble Model

[...]

C. Becchi, A. Rouet, R. Stora
01 Jan 1975
TL;DR: In this paper, the perturbative renormalization of the abelian Higgs-Kibble model is studied within the class of renormalizable gauges which are odd under charge conjugation.
Abstract: This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

747 citations

Journal Article•DOI•
Gauge string fields from the light cone

[...]

Warren Siegel1, Barton Zwiebach2•
University of Maryland, College Park1, Massachusetts Institute of Technology2
01 Jan 1987-Nuclear Physics
TL;DR: In this article, a method for deriving general gauge-invariant field theories from light-cone representations of the Poincare algebra at x + = 0 is described.

162 citations

Journal Article•DOI•
Nonperturbative properties of Yang-Mills theories

[...]

Markus Q. Huber1, Markus Q. Huber2•
University of Giessen1, University of Graz2
03 Oct 2020-Physics Reports
TL;DR: In this article, the results of correlation functions in the Landau gauge obtained from their equations of motions are discussed and compared to the results obtained in other covariant and maximally Abelian gauges.

90 citations

Journal Article•DOI•
Algorithmic derivation of Dyson-Schwinger equations

[...]

Reinhard Alkofer1, Markus Q. Huber1, Kai Schwenzer1•
University of Graz1
01 Jun 2009-Computer Physics Communications
TL;DR: The Mathematica package DoDSE 1 is introduced which derives the Dyson–Schwinger equations graphically once the interactions of the theory are specified and is suitable for an implementation within a symbolic programming language.

58 citations

Posted Content•
Nonperturbative properties of Yang-Mills theories

[...]

Markus Q. Huber1, Markus Q. Huber2•
University of Graz1, University of Giessen2
15 Aug 2018-arXiv: High Energy Physics - Phenomenology
TL;DR: In this article, the results of correlation functions in the Landau gauge obtained from their equations of motions are discussed and compared to the results obtained in other covariant and maximally Abelian gauges.
Abstract: Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson-Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang-Mills theories.

50 citations

Additional excerpts

  • ...[605–608] is employed: Γ μ (k; p, q) = i g f abc (η pμ − η̂ qμ) (290) with η + η̂ = 1....

    [...]

References
More filters
Renormalization of the Abelian Higgs-Kibble Model

[...]

C. Becchi, A. Rouet, R. Stora
01 Jan 1975
TL;DR: In this paper, the perturbative renormalization of the abelian Higgs-Kibble model is studied within the class of renormalizable gauges which are odd under charge conjugation.
Abstract: This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

747 citations

Journal Article•DOI•
Operator anomaly for the gauss law

[...]

L. D. Faddeev1•
Scuola Normale Superiore di Pisa1
13 Sep 1984-Physics Letters B
TL;DR: In this paper, it was shown that a Schwinger term can appear in the commutation relations of constraints for the theory of the interacting Yang-Mills field and chiral fermions.

409 citations

Journal Article•DOI•
Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras

[...]

M. Scheunert, W. Nahm, V. Rittenberg
01 Jan 1977-Journal of Mathematical Physics
TL;DR: In this paper, the authors illustrate the differences between the properties of the irreducible representations of simple graded Lie algebras and simple simple Lie algesbras.
Abstract: We illustrate through the examples of the osp(2,1) and spl(2,1) algebras the differences between the properties of the irreducible representations of simple graded Lie algebras and simple Lie algebras.

293 citations

Journal Article•DOI•
Superfield formulation of extended BRS symmetry

[...]

Loriano Bonora1, M. Tonin1•
Istituto Nazionale di Fisica Nucleare1
01 Jan 1981-Physics Letters B
TL;DR: In this article, a superfield treatment of lagrangian gauge theories supplemented by gauge fixings and Faddeev-Popov terms is presented, and a new BRS-like symmetry in gauge theories is discovered.

280 citations

Journal Article•DOI•
The principle of BRS symmetry: An alternative approach to Yang-Mills theories

[...]

L. Baulieu1, Jean Thierry-Mieg2•
Columbia University1, Harvard University2
12 Apr 1982-Nuclear Physics
TL;DR: The most general BRS and anti-BRS admissible gauges are linear in the gauge field, but may depend non-linearly on the ghost fields as mentioned in this paper, and they also give a heuristic interpretation of the BRS symmetry.

235 citations

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The infrared behaviour of QCD Green's functions ☆: Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

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01 Nov 2001-Physics Reports
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Quantization of non-Abelian gauge theories

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Infrared exponent for gluon and ghost propagation in Landau gauge QCD

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03 Jun 2002-Physical Review D
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Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories.

[...]

18 Jun 2008-Physical Review Letters
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Frequently Asked Questions (1)
Q1. What are the contributions in this paper?

The authors study the ghost antighost symmetry of the extended BRS equations, discuss the geometrical interpretation of the formalism and define a new class of gauges in which the ghost number is only conserved modulo two. LThis work was supported by the Director, Office of Energy Research Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U. S. Department of Energy under Contract DE-AC0376SF00098.