The Dyson-Schwinger equation of a link variable in lattice Landau gauge theory

Sternbeck, André; Schaden, Martin; Mader, Valentin

doi:10.22323/1.214.0354

Cited by 5 publications

(11 citation statements)

References 3 publications

(4 reference statements)

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“…This additional term only contributes at low momenta. This is consistent with the observations in [30].…”

Section: Summary and Discussionsupporting

confidence: 94%

“…The difference is that all ingredients in (4) are determined using lattice methods, and it is checked, whether the left-hand-side is indeed zero, rather than to leave one element to be determined using the functional equations. In this sense, it is closer to [30] in spirit. It is also different from [30] in the following sense.…”

Section: Basic Ideamentioning

confidence: 85%

“…In this sense, it is closer to [30] in spirit. It is also different from [30] in the following sense. There, only quantities directly calculated on the lattice enter a DSE for the link.…”

Section: Basic Ideamentioning

confidence: 85%

“…The input propagators are shown in appendix B for three and four dimensions. For two dimensions these are the same as in [26] It is important to note that a similar idea was pursued in a forward direction in [30]. There, the DSE for the link on a discrete lattice was derived for the pure Landau gauge condition.…”

Section: Introductionmentioning

confidence: 99%

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Constraining the gauge-fixed Lagrangian in minimal Landau gauge

Maas

2020

SciPost Phys.

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A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.

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“…This additional term only contributes at low momenta. This is consistent with the observations in [30].…”

Section: Summary and Discussionsupporting

confidence: 94%

Section: Basic Ideamentioning

confidence: 85%

“…In this sense, it is closer to [30] in spirit. It is also different from [30] in the following sense. There, only quantities directly calculated on the lattice enter a DSE for the link.…”

Section: Basic Ideamentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Constraining the gauge-fixed Lagrangian in minimal Landau gauge

Maas

2020

SciPost Phys.

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“…The question then arises: which if any numerical gauge choice corresponds to the GZ action with its horizon condition [24] ? In numerical studies, gauge fixing is done by taking a configuration A generated by a standard gauge-invariant Monte Carlo procedure, and minimizing the Hilbert square norm ||A|| 2 with respect to local gauge transformations g, by some numerically convenient minimization procedure so a relative minimum A 1 is achieved.…”

Section: Comparison With the Lattice Datamentioning

confidence: 99%

Spectral decomposition of the ghost propagator and a necessary condition for confinement

Cooper¹,

Zwanziger²

2016

Phys. Rev. D

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In this article we present exact calculations that substantiate a clear picture relating the confining force of QCD to the zero-modes of the Faddeev-Popov (FP) operator M (gA) = −∂ · D(gA). This is done in two steps. First we calculate the spectral decomposition of the FP operator and show that the ghost propagator G(k;gA) = k|M −1 (gA)| k in an external gauge potential A is enhanced at low k in Fourier space for configurations A on the Gribov horizon. This results from the new formula in the low-k regime G ab (k, gA) = δ ab λ −1 | k| (gA), where λ | k| (gA) is the eigenvalue of the FP operator that emerges from λ | k| (0) = k 2 at A = 0. Next we derive a strict inequality signaling the divergence of the color-Coulomb potential at low momentum k namely, V (k) ≥ k 2 G 2 (k) for k → 0, where V (k) is the Fourier transform of the color-Coulomb potential V (r) and G(k) is the ghost propagator in momentum space. Although the color-Coulomb potential is a gauge-dependent quantity, we recall that it is bounded below by the gauge-invariant Wilson potential, and thus its long range provides a necessary condition for confinement. The first result holds in the Landau and Coulomb gauges, whereas the second holds in the Coulomb gauge only.

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More on the properties of the first Gribov region in Landau gauge

Maas

2016

Phys. Rev. D

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Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.Comment: 42 pages, 23 figures, 1 tabl

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The Dyson-Schwinger equation of a link variable in lattice Landau gauge theory

Abstract: We derive the Dyson-Schwinger equation of a link variable in SU(n) lattice gauge theory in minimal Landau gauge and confront it with Monte-Carlo data for the different terms. Preliminary results for the lattice analog of the Kugo-Ojima confinement criterion is also shown.

Cited by 5 publications

References 3 publications

Constraining the gauge-fixed Lagrangian in minimal Landau gauge

Constraining the gauge-fixed Lagrangian in minimal Landau gauge

Spectral decomposition of the ghost propagator and a necessary condition for confinement

More on the properties of the first Gribov region in Landau gauge

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