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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
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Journal Article•
Non-perturbative Propagators, Running Coupling and Dynamical Mass Generation in Ghost-Antighost Symmetric Gauges in QCD

[...]

Christian S. Fischer
23 Apr 2003-arXiv: High Energy Physics - Phenomenology
TL;DR: In this article, the authors present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson-Schwinger equations.
Abstract: We present approximate non-perturbative solutions for the propagators as well as the running coupling of QCD from a coupled system of renormalised, truncated Dyson--Schwinger equations. We employ ansaetze for the dressed vertices such that the running coupling and the quark mass function are independent of the renormalisation point. Our solutions are in good agreement with the results of recent lattice calculations. We find a weakly vanishing gluon propagator at small momenta and an infrared singular ghost propagator in agreement with Zwanziger's horizon condition and the Kugo-Ojima confinement criterion. The running coupling possesses an infrared fixed point at alpha(0) = 8.92/N_c. To investigate the influence of boundary conditions on the propagators we solved the ghost and gluon DSEs also on a four-torus. Our results show typical finite volume effects but are still close to the continuum solutions for sufficiently large volumes. For the quark propagator we find dynamically generated quark masses that agree well with phenomenological values. The effects of unquenching the system are found to be small. In particular the infrared behaviour of the ghost and gluon dressing functions found in pure Yang-Mills theory is almost unchanged as long as the number of light flavors is smaller than four.

43 citations

Journal Article•DOI•
On the infrared scaling solution of SU(N) Yang-Mills theories in the maximally Abelian gauge

[...]

Markus Q. Huber1, Kai Schwenzer2, Reinhard Alkofer1•
University of Graz1, University of Washington2
12 Apr 2009-arXiv: High Energy Physics - Theory
TL;DR: In this article, an improved method for extracting infrared exponents from functional equations is presented, which allows for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge.
Abstract: An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators' infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost anti-ghost symmetric gauges.

36 citations

Journal Article•DOI•
On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge

[...]

Markus Q. Huber1, Kai Schwenzer2, Reinhard Alkofer1•
University of Graz1, University of Washington2
30 Jun 2010-European Physical Journal C
TL;DR: In this article, an improved method for extracting infrared exponents from functional equations is presented, which allows for an analysis of quite complicated systems such as Yang-Mills theory in the maximally Abelian gauge.
Abstract: An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang–Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators’ infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost–anti-ghost symmetric gauges.

30 citations

Journal Article•DOI•
Spurious divergences in Dyson-Schwinger equations

[...]

Markus Q. Huber1, Markus Q. Huber2, Lorenz von Smekal1, Lorenz von Smekal2•
Technische Universität Darmstadt1, University of Giessen2
14 Apr 2014-Journal of High Energy Physics
TL;DR: In this article, the authors revisited the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance.
Abstract: We revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green’s functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

29 citations

Journal Article•DOI•
Curci–Ferrari mass and the Neuberger problem

[...]

Alexander C. Kalloniatis1, L. von Smekal2, Anthony G. Williams1•
University of Adelaide1, University of Erlangen-Nuremberg2
10 Mar 2005-Physics Letters B
TL;DR: In this article, the massive Curci-Ferrari model was used as a starting point for defining BRST quantization for Yang-Mills theory on the lattice.

28 citations

References
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Journal Article•DOI•
Consequences of anomalous ward identities

[...]

Julius Wess1, Julius Wess2, Bruno Zumino2•
Karlsruhe Institute of Technology1, CERN2
01 Nov 1971-Physics Letters B
TL;DR: In this paper, the anomalous Ward identities are shown to satisfy consistency or integrability relations, which restrict their possible form, for the case of SU(3) × SU(1) and for SU(2) + SU (3) + 2.

2,450 citations

Journal Article•DOI•
Feynman Diagrams for the Yang-Mills Field

[...]

L. D. Faddeev, V.N. Popov
24 Jul 1967-Physics Letters B
TL;DR: In this paper, a simple method for calculation of the contribution from arbitrary diagrams with closed loops was proposed, based on the method of Feynman functional integration, which is used in this paper.

1,646 citations

Journal Article•DOI•
Renormalization of gauge theories

[...]

C. Becchi1, A. Rouet1, R. Stora1•
Centre national de la recherche scientifique1
01 Jun 1976-Annals of Physics
TL;DR: Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts as mentioned in this paper.

1,551 citations

Journal Article•DOI•
Renormalization of the Abelian Higgs-Kibble Model

[...]

C. Becchi, A. Rouet, R. Stora
01 May 1975-Communications in Mathematical Physics
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.

1,045 citations

Journal Article•DOI•
Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem

[...]

Taichiro Kugo1, Izumi Ojima2•
Kyoto University1, Research Institute for Mathematical Sciences2
01 Feb 1979-Progress of Theoretical Physics Supplement
TL;DR: A manifestly covariant and local canonical operator formalism of non-Abelian gauge theories is presented in this paper, which is applicable to Yang-Mills theories as well as to gravity.
Abstract: A manifestly covariant and local canonical operator formalism of non-Abelian gauge theories is presented in its full detail. This formalism, applicable to Yang-Mills theories as well as to gravity, not only provides us a transparent understanding in the scattering theoretical aspects, but also makes it possible to discuss other important problems directly related to the (Heisenberg) operators and the state vectors: As for the former, the physical S-matrix unitarity is proved quite generally on the basis of the representation of the algebra of the BRS charge, and asymptotic field analysis is explicitly performed for some examples. As for the latter, the problems of observables and the well-definedness of charge operators are discussed and clear results are obtained, where the locality and covariance of the formalism are indispensable. Observables are shown to be invariant under the BRS transformation as well as the unbroken global gauge groups. By analyzing the structure of “Maxwell” equations in YM theories, the converse of the Higgs theorem is found to hold. This turns out to lead to a remarkably simple criterion of quark confinement in QCD. The present formalism is found useful also for the U(1) problem and the charge universality proof in the Weinberg-Salam model. General theory of indefinite metric quantum fields is developed to some extent.

923 citations

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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.