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Nonperturbative Landau gauge and infrared critical exponents
 in QCD, [hepth/0109224], Phys. Rev. D65, 094039
, 2002
"... We discuss FaddeevPopov quantization at the nonperturbative level and show that Gribov’s prescription of cutting off the functional integral at the Gribov horizon does not change the SchwingerDyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov ..."
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We discuss FaddeevPopov quantization at the nonperturbative level and show that Gribov’s prescription of cutting off the functional integral at the Gribov horizon does not change the SchwingerDyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov’s prescription is not exact, and we therefore turn to the method of stochastic quantization in its timeindependent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the FaddeevPopov method in Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled SchwingerDyson equations for the gluon and ghost propagators D(k) and G(k) in Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by D(k) ∼ 1/(k 2) 1+aD 1/(k 2) 1+aG and G(k) ∼ are obtained in spacetime dimensions d = 2, 3, 4. Two possible solutions are obtained with the values, in d = 4 dimensions, aG = 1, aD = −2, or aG = (93 − 1201)/98 ≈ 0.595353, aD = −2aG
Gribov copies in the minimal Landau gauge: the influence on gluon and ghost propagators, Nucl. Phys. B508
, 1997
"... 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 th ..."
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Cited by 10 (3 self)
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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 strongcoupling 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 gaugerelated 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