Properties of gauge orbits

Maas, Axel

doi:10.22323/1.105.0279

Cited by 11 publications

(34 citation statements)

References 11 publications

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“…However, due to subtleties related to the definition of the step-function it is not yet proven that this is a valid procedure, though it has many interesting properties, and has been investigated in great detail, see e. g. [67,[70][71][72][73][74][75][76][77][78][79][80][81][82] and especially the review [17]. Furthermore, no Gribov copy, or any gauge copy in general, is preferred compared to another [83]. It would thus be completely legitimate to always chose the innermost Gribov copy for each gauge orbit.…”

Section: Proposals For Resolving the Gribov-singer Ambiguity 251 Gmentioning

confidence: 99%

“…Assuming the choice to be ergodic, unbiased, and well-behaved, this implies that this prescription is equivalent to averaging over the residual gauge orbit [91,93]. However, a constructive prescription how to make this choice in a path integral formulation is only developing [83,91,93]. Precise definitions of this gauge therefore exist only as operational definitions in terms of algorithms in lattice gauge theory [102].…”

Section: Minimal Landau Gaugementioning

confidence: 99%

“…But neither the existence nor the form of such a construction has yet been proven, there exists only proposals for it [83,91].…”

Section: Landau-b Gaugesmentioning

confidence: 99%

“…Instead, at best it can only be imposed that the condition < b >= B can be satisfied, but not b = B. This can be implemented in the path-integral by using a Lagrange parameter 19 λ(B), like temperature, as a gauge parameter, which gives (26) the form [83,91,93]…”

Section: Landau-b Gaugesmentioning

confidence: 99%

“…It is associated with the center symmetry Z N of SU(N) theory 83 , being non-zero if the symmetry is broken [191].…”

Section: Order Parametersmentioning

confidence: 99%

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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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Section: Proposals For Resolving the Gribov-singer Ambiguity 251 Gmentioning

confidence: 99%

Section: Minimal Landau Gaugementioning

confidence: 99%

“…But neither the existence nor the form of such a construction has yet been proven, there exists only proposals for it [83,91].…”

Section: Landau-b Gaugesmentioning

confidence: 99%

Section: Landau-b Gaugesmentioning

confidence: 99%

“…It is associated with the center symmetry Z N of SU(N) theory 83 , being non-zero if the symmetry is broken [191].…”

Section: Order Parametersmentioning

confidence: 99%

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Gauge bosons at zero and finite temperature

2013

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On the gauge boson’s properties in a candidate technicolor theory

Maas

2011

J. High Energ. Phys.

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The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is twotechnicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks.Using lattice gauge theory the properties of the technigluons in this scenario are investigated as a function of the techniquark mass towards the massless limit. For that purpose the minimal Landau gauge two-point and three-point correlation functions are determined, including a detailed systematic error analysis.The results are, within the relatively large systematic uncertainties, compatible with a behavior very similar to QCD at finite techniquark mass. However, the limit of massless techniquarks exhibits features which could be compatible with a (quasi-)conformal behavior.

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No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

2012

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We study general properties of the Landau-gauge Gribov ghost form factor ðp 2 Þ for SUðN c Þ Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d ¼ 3, 4 with respect to the d ¼ 2 case. In particular, considering any (sufficiently regular) gluon propagator Dðp 2 Þ and the one-loop-corrected ghost propagator, we prove in the 2d case that the function ðp 2 Þ blows up in the infrared limit p ! 0 as ÀDð0Þ lnðp 2 Þ. Thus, for d ¼ 2, the no-pole condition ðp 2 Þ < 1 (for p 2 > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, Dð0Þ ¼ 0. On the contrary, in d ¼ 3 and 4, ðp 2 Þ is finite also if Dð0Þ > 0. The same results are obtained by evaluating the ghost propagator Gðp 2 Þ explicitly at one loop, using fitting forms for Dðp 2 Þ that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g 2 as a free parameter, the ghost propagator admits a one-parameter family of behaviors ( labeled by g 2 ), in agreement with previous works by Boucaud et al. In this case the condition ð0Þ 1 implies g 2 g 2 c , where g 2 c is a ''critical'' value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g 2 smaller than g 2 c , while for g 2 ¼ g 2 c one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for ðp 2 Þ and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor ðp 2 Þ. Using these bounds we find again that only in the d ¼ 2 case does one need to impose Dð0Þ ¼ 0 in order to satisfy the no-pole condition. The d ¼ 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d ¼ 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result Dð0Þ ¼ 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

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Properties of gauge orbits

Cited by 11 publications

References 11 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

On the gauge boson’s properties in a candidate technicolor theory

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the2dgluon propagator

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