Infrared behavior and Gribov ambiguity in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>lattice gauge theory

Bornyakov, V. G.; Mitrjushkin, V.K.; Müller–Preussker, M.

doi:10.1103/physrevd.79.074504

Cited by 73 publications

(144 citation statements)

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“…In this case the representative is selected which minimizes a certain non-local functional (the integral of the trace of the gluon propagator [7]) absolutely, though this has still a minor problem with topological identifications of certain gauge copies. It has been conjectured that for correlation functions made from a finite polynominal of the gauge fields this should yield the same correlation function as the minimal Landau gauge [8], which is supported by available results [11].…”

Section: The Example Of Landau Gauge(s)supporting

confidence: 53%

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Properties of gauge orbits

Maas¹

2011

Proceedings of the XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010)

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Gauge fixing is a useful tool to simplify calculations. It is also valuable to combine different methods, in particular lattice and continuum methods. However, beyond perturbation theory the Gribov-Singer ambiguity requires further gauge conditions for a well-defined gauge-fixing prescription. Different additional conditions can, in principle, lead to different results for gaugedependent correlation functions, as will be discussed for the example of Landau gauge. Also the relation of lattice and continuum gauge fixing beyond perturbation theory will be briefly outlined.

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Section: The Example Of Landau Gauge(s)supporting

confidence: 53%

“…• Absolute Landau gauge [7,8,11]. In this case the representative is selected which minimizes a certain non-local functional (the integral of the trace of the gluon propagator [7]) absolutely, though this has still a minor problem with topological identifications of certain gauge copies.…”

Section: The Example Of Landau Gauge(s)mentioning

confidence: 99%

Properties of gauge orbits

Maas¹

2011

Proceedings of the XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010)

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“…Studies of such artifacts due to volume effects and discretization effects can be found, e. g., in [91,96,118,122,123,204,258]. The major contribution of the artifacts is due to finitevolume effects.…”

Section: Correlation Functions 411 Propagatorsmentioning

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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“…Our lattice data are consistent with this behavior. On the other hand, lattice studies done at h = 0 in d = 3 and 4 dimensions [3][4][5][6][7][8], including the present study, give a finite value for the gluon propagator at zero momentum, lim k→0 D(k, 0) > 0. So, if one takes the lattice data at face value, there must be a jump in the low momentum limit of the gluon propagator at h = 0.…”

Section: Discussionmentioning

confidence: 99%

“…At the same time, lattice calculations, which do not need external sources, found this propagator to be finite, at least in three and four dimensions 1 [3][4][5][6][7][8] for a review.…”

Section: Introductionmentioning

confidence: 99%

Analytic and numerical study of the free energy in gauge theory

Maas

Zwanziger

2014

Phys. Rev. D

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at h = 0 and k = 0, and the value of D(k, h) at this point depends on the order of limits. We also present numerical evaluations of the free energy W (k, h) and the gluon propagator D(k, h) for the case of SU(2) Yang-Mills theory in various dimensions which support all of these findings.PACS numbers: 11.10. Kk; 11.15.Ha; 12.38.Aw; 14.70.Dj * Supported by the DFG under grant number MA 3935/5-1; axelmaas@web.de † dz2@nyu.edu 2 I. INTRODUCTIONThe free energy, and its Legendre transform, the quantum effective action, play a central role in quantum field theories. As the generating functionals of correlation functions, their knowledge, in principle, grants access to all there is to know about a theory. It is often assured that these functionals are analytic in their external sources, at least away from phase transitions, and thus their derivatives yield, in a well-defined manner, the correlation functions.However, recently this assumption yielded colliding results: Assuming this analyticity, the minimal Landau gauge gluon propagator has necessarily to vanish at zero (Euclidean) momentum [1,2]. At the same time, lattice calculations, which do not need external sources, found this propagator to be finite, at least in three and four dimensions 1 [3-8] for a review.At the same time, continuum calculations using functional methods, where the functional equations were derived under this assumption, found both solutions [14][15][16][17][18]. See [9] for a review of the situation.The logical starting point to resolve this discrepancy is therefore to check the analyticity of the free energy. This is the aim in this work.To this end, we shall be concerned with the Euclidean correlators of gluons in QCD with an arbitrary gauge group, here chosen to be SU(N), for the local gauge symmetry that are fixed to the minimal Landau gauge. These are the fundamental quantities in quantum field theory.The minimal Landau gauge [9] is obtained by minimizing the Hilbert square normto some local minimum (in general not an absolute minimum) with respect to local gauge transformations g(x). These act according tog A|| 2 is stationary and its second variation is positive. It is well known that these two properties imply respectively that the Landau gauge (transversality) condition is satisfied, ∂ · A = 0, and that the Faddeev-Popov operator is positive i. e.(ω, M(A)ω) ≥ 0 for all ω. Here the Faddeev-Popov operator acts according to [9] that in general there are more than one local minimum of F A (g), and we do not specify which local minimum is achieved. This gauge is realized numerically by minimizing a lattice analog of F A (g) by some algorithm, and the local minimum achieved is in general algorithm dependent. However, for all commonly employed algorithms this does not yield different expectation values, as they all are equivalent to an averaging over the first Gribov region [9,20].The analytic bounds which we shall obtain in section II follow from the restriction of the gauge-fixed configurations to the Gribov region Ω, and are the same wheth...

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Infrared behavior and Gribov ambiguity inSU(2)lattice gauge theory

Cited by 73 publications

References 55 publications

Properties of gauge orbits

Properties of gauge orbits

Gauge bosons at zero and finite temperature

Analytic and numerical study of the free energy in gauge theory

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