Numerical study of the fundamental modular region in the minimal Landau gauge

Cucchieri, Attilio

doi:10.1016/s0550-3213(98)00235-1

Cited by 39 publications

(60 citation statements)

References 27 publications

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“…Let us recall that evidences of Gribov-copy effects in lattice Landau gauge have been found by various authors [24,54,55,56,57] for the ghost propagator and, recently, also for the gluon propagator [53,57], these effects being usually stronger at small momenta. Such effects have also been found [50,54] for the horizon tensor (and for the horizon function), for the smallest eigenvalue of the Faddeev-Popov matrix, for the Kugo-Ojima parameter and for the running coupling constant (defined using gluon and ghost propagators).…”

Section: Simulationsmentioning

confidence: 71%

“…[26]), then our value of β corresponds to β ≈ 2.21 in the four dimensional case. In this work we did not do a systematic study of Gribov-copy effects [24,50,51,52,53,54,55,56,57] for the two propagators, since here we are interested in possible systematic effects due to the use of asymmetric lattices. Let us recall that evidences of Gribov-copy effects in lattice Landau gauge have been found by various authors [24,54,55,56,57] for the ghost propagator and, recently, also for the gluon propagator [53,57], these effects being usually stronger at small momenta.…”

Section: Simulationsmentioning

confidence: 99%

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Infrared behavior of gluon and ghost propagators from asymmetric lattices

Cucchieri

Mendes

2006

Phys. Rev. D

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We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU (2) gauge theory. Data have been obtained using asymmetric lattices (V = 20 2 ×60, 40 2 ×60, 8 2 × 64, 8 2 × 140, 12 2 × 140 and 16 2 × 140) for the lattice coupling β = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V . By comparing these results with data obtained using symmetric lattices (V = 60 3 and 140 3 ), we find that both propagators suffer from systematic effects in the infrared region (p 650MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

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Section: Simulationsmentioning

confidence: 71%

Section: Simulationsmentioning

confidence: 99%

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Cucchieri

Mendes

2006

Phys. Rev. D

Self Cite

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“…Based on this observation, the absolute Landau gauge is defined as selecting the Gribov copy which belongs to the fundamental modular domain [106,107]. This condition can be realized by either checking the absolute minimization of (23) explicitly or by the introduction of a suitable weight factor in the path integral [108].…”

Section: Raw Distribution Of F(a) In Four Dimensionsmentioning

confidence: 99%

“…The condition (107) immediately implies that the ghost is unphysical. The condition (107) implies that the gluon in two dimensions is unphysical, since when a propagator vanishes at zero momentum, the spectral function cannot be positive. The condition from (109) at n = 1 implies that the gluon is not a physical particle in three dimensions, since the propagator is non-monotonous and therefore its first derivative changes sign [79].…”

Section: Schwinger Functions Mass and Asymptotic Statesmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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“…Nevertheless, for the purpose of calculating propagators it is likely that this condition is sufficient for eliminating Gribov copies [15]. Note that, in lattice calculations, the Gribov ambiguity poses a more severe problem and makes it especially hard to extract the ghost propagator [31].…”

Section: Constraints On the Solutionsmentioning

confidence: 99%

High-temperature limit of Landau-gauge Yang-Mills theory

et al. 2004

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Abstract. The infrared properties of the high-temperature limit of Landau-gauge Yang-Mills theory are investigated. In a first step the high-temperature limit of the Dyson-Schwinger equations is taken. The resulting equations are identical to the Dyson-Schwinger equations of the dimensionally reduced theory, a three-dimensional Yang-Mills theory coupled to an effective adjoint Higgs field. These equations are solved analytically in the infrared and ultraviolet, and numerically for all Euclidean momenta. We find infrared enhancement for the Faddeev-Popov ghosts, infrared suppression for transverse gluons and a mass for the Higgs. These results imply long-range interactions and over-screening in the chromomagnetic sector of high temperature Yang-Mills theory while in the chromoelectric sector only screening is observed.

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Numerical study of the fundamental modular region in the minimal Landau gauge

Cited by 39 publications

References 27 publications

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Infrared behavior of gluon and ghost propagators from asymmetric lattices

Gauge bosons at zero and finite temperature

High-temperature limit of Landau-gauge Yang-Mills theory

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