More (thoughts on) Gribov copies

Baal, Pierre van

doi:10.1016/0550-3213(92)90386-p

Cited by 197 publications

(318 citation statements)

References 22 publications

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“…From these works we also know that Ω is simply the region of local minima of the functional E A [g], namely it includes Λ, and is not free of Gribov copies. It has also been shown [20] that in the interior of the fundamental modular region Λ the absolute minima are non-degenerate. However, on the boundary of Λ there are degenerate absolute minima, and they have to be identified in order to obtain a region truly free of Gribov copies.…”

Section: Minimal Landau Gaugementioning

confidence: 99%

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Gribov copies in the minimal Landau gauge: The influence on gluon and ghost propagators

1997

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We study the influence of Gribov copies on gluon and ghost propagators, evaluated numerically in pure SU (2) lattice gauge theory in the minimal Landau gauge. Simulations are done at four different values of β (namely β = 0, 0.8, 1.6 and 2.7 ) and for volumes up to 16 4 (up to 24 4 at β = 1.6). For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy, even at very small values of the coupling β. On the contrary, for the ghost propagator, Gribov noise is clearly observable for the three values of β in the strong-coupling regime. In particular, data corresponding to the minimal Landau gauge are always smaller than those obtained in a generic Landau gauge. This result can be qualitatively explained.Gauge theories, being invariant under local gauge transformations, are systems with redundant dynamical variables, which do not represent true dynamical degrees of freedom. The objects of interest are not the gauge fields themselves, but rather the classes (orbits) of gauge-related fields. The elimination of such redundant gauge degrees of freedom is essential for understanding and extracting physical information from these theories. This is usually done by a method called gauge fixing, which is based on the assumption that a gauge-fixing condition can be found which uniquely determines a representative gauge field on each orbit. It was pointed out by Gribov [1] that the standard gauge-fixing conditions used for perturbative calculations do not in fact fix the gauge fields uniquely: for a non-abelian gauge theory, in the Coulomb or in the Landau gauge, there are many gauge equivalent configurations satisfying the Coulomb or Landau transversality condition. The existence of these Gribov copies does not affect the results from perturbation theory, but their elimination could play a crucial role for non-perturbative features of these theories.One of the celebrated advantages of lattice gauge theories is that the lattice provides a regularization which makes the gauge group compact, so that the Gibbs average of any gauge-invariant quantity is well-defined and therefore gauge fixing is, in principle, not required. However, because

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Section: Minimal Landau Gaugementioning

confidence: 99%

“…In this way, the condition x ψ a (x) = 0 is automatically imposed, and at the same time we save computer time by evaluating "half" of the Fourier transform in eq. (20).…”

Section: Propagators On the Latticementioning

confidence: 99%

Gribov copies in the minimal Landau gauge: The influence on gluon and ghost propagators

1997

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“…is well defined and differentiable along the gauge orbit of A i is at the basis of well established results concerning the properties of the Gribov and fundamental modular regions in the Landau gauge, see [6,7,8]. The Gribov region corresponds in fact to the set of all relative minima of the functional f A [U ] in the space of the gauge orbits, while the fundamental modular region is defined as the set of all absolute minima of f A [U ].…”

Section: Introductionmentioning

confidence: 99%

A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges

Guimaraes

Sorella

2011

Journal of Mathematical Physics

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The construction outlined by Henyey [1] is employed to provide examples of normalizable zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges in SU (2) Euclidean YangMills theories in d = 3 dimensions. The corresponding gauge configurations have all finite norm ||A|| 2 < ∞. In particular, in the case of the Landau gauge, the explicit construction of an infinite class of normalizable zero modes with finite norm ||A|| 2 is provided. * msguimaraes@uerj.br † sorella@uerj.br ‡ Work supported by FAPERJ, Fundação de Amparoà Pesquisa do Estado do Rio de Janeiro, under the program Cientista do Nosso Estado, E-26/101.578/2010.

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“…To resolve this Gribov proposed that the path integral be restricted to the region defined by the first zero of the FaddeevPopov operator which is defined as the Gribov volume. Whilst one can still have gauge copies inside the Gribov horizon, [18][19][20], within it there is a smaller region known as the fundamental modular region where there are no Gribov copies. The key feature of the restriction to the first Gribov region is the introduction of the Gribov mass scale, γ, which can be related to the volume of the first Gribov region.…”

Section: Introductionmentioning

confidence: 99%