Quantitative comparison of filtering methods in lattice QCD

Bruckmann, Falk; Gattringer, Christof; Ilgenfritz, Ernst-Michael; Müller–Preussker, M.; Schäfer, Andreas; Solbrig, Stefan

doi:10.1140/epja/i2007-10459-5

Cited by 37 publications

(77 citation statements)

References 9 publications

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“…In [91,348]. Already at about 100 smearing steps, the configurations are essential self-dual [345], and thus approximately pure topological configurations. Results are for a V = (2.5 fm)…”

Section: Relations To Topological Structuresmentioning

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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“…In [91,348]. Already at about 100 smearing steps, the configurations are essential self-dual [345], and thus approximately pure topological configurations. Results are for a V = (2.5 fm)…”

Section: Relations To Topological Structuresmentioning

confidence: 99%

“…Complementary to analytical methods, lattice simulations provide a possibility to access the topological content of a field configuration by smearing and projecting, at least in an approximate way [191,345,346]. The so treated field configurations become self-dual, which classifies them as topological [2,347].…”

Section: Relations To Topological Structuresmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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“…This comparison will lead us to a one-to-one mapping of the ultraviolet cutoff cut (mode truncation in the overlap picture) to the number of stout-link smearing iterations over a wide range of smearing iterations. In a similar spirit, the correspondence of APE smearing [19,20], Laplacian filtering [21], and the topological density filtered according to another Ginsparg-Wilson-Dirac operator [22,23] has been studied recently [24,25].…”

Section: Introductionmentioning

confidence: 99%

Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD

et al. 2008

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A detailed comparison is made between the topological structure of quenched QCD as revealed by the recently proposed over-improved stout-link smearing in conjunction with an improved gluonic definition of the topological density on one hand and a similar analysis made possible by the overlap-fermionic topological charge density both with and without variable ultraviolet cutoff cut . The matching is twofold, provided by fitting the density-density two-point functions on one hand and by a point-by-point fitting of the topological densities according to the two methods. We point out the similar cluster structure of the topological density for moderate smearing and 200 MeV < cut < 600 MeV, respectively. We demonstrate the relation of the gluonic topological density for extensive smearing to the location of the overlap zero modes and the lowest overlap nonzero mode as found for the unsmeared configurations.

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“…In recent work Gattringer, Ilgenfritz and their collaborators [2,3,4] use eigenmodes to compare filtering methods and properties of topological excitations. Anna Hasenfratz et al [5] draw the attention to the role played by the localized eigenmodes.…”

Section: Introductionmentioning

confidence: 99%

Interactive Visualization Package for 4D LFTs

Hip¹

2008

Proceedings of the XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007)

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Recent interest in exploring local vacuum structure of QCD through the properties of the eigenmodes of the lattice Dirac operators rises again the challenge to visualize four-dimensional objects and structures which appear in lattice field theories. In spite of complex and powerful commercial visualization software packages on the market, there are reasons to develop Interactive Visualization Package (IVP). We believe that an apprehension of the complex structures is possible only through the interactive approach, with the user being able to manipulate data representations and slices through the lattice in real-time. Further insight should also be gained by an interactive parallel examination of different physical quantities, e.g. eigenmode density with topological charge or action densities. Finally, thanks to constantly falling hardware prices, IVP makes it possible to use almost any Linux PC as a visualization tool for research in lattice field theory. The XXV International Symposium on Lattice Field Theory

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Quantitative comparison of filtering methods in lattice QCD

Cited by 37 publications

References 9 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Vacuum structure revealed by over-improved stout-link smearing compared with the overlap analysis for quenched QCD

Interactive Visualization Package for 4D LFTs

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