Schwinger-Dyson equations and disorder

Szczepaniak, Adam P.; Reinhardt, Hugo

doi:10.1103/physrevd.84.056011

Cited by 5 publications

(5 citation statements)

References 41 publications

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“…The resolution of the energy behaviour of this correlation function is a quite delicate point which requires a detailed mastering of the renormalization procedure of the Coulomb gauge. Here, we remind the reader to the large literature existing on this subject, both in the continuum as well as in the lattice formulation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”

Section: The Gribov-zwanziger Action In the Coulomb Gaugementioning

confidence: 99%

Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

2015

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We investigate the dimension two condensate φab i φ ab i −ω ab i ω ab i within the Gribov-Zwanziger approach to Euclidean Yang-Mills theories in the Coulomb gauge, in both 3 and 4 dimensions. An explicit calculation shows that, at the first order, the condensate φab i φ ab i −ω ab i ω ab i is plagued by a non-integrable IR divergence in 3D, while in 4D it exhibits a logarithmic UV divergence, being proportional to the Gribov parameter γ 2 . These results indicate that in 3D the transverse spatial Coulomb gluon two-point correlation function exhibits a scaling behaviour, in agreement with Gribov's expression. In 4D, however, they suggest that, next to the scaling behaviour, a decoupling solution might emerge too.

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Section: The Gribov-zwanziger Action In the Coulomb Gaugementioning

confidence: 99%

Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

2015

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“…A recent development in the ongoing study of the basic QCD Green's functions within the nonperturbative framework of the Schwinger-Dyson equations (SDEs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] is the derivation of the particular integral equation that governs the momentum evolution of the effective gluon mass [19][20][21][22]. As has been argued in a series of works [23][24][25][26], the generation of such a mass offers a natural and self-consistent explanation for the infrared finiteness of the (Landau gauge) gluon propagator and ghost dressing function [11,19,20,27,28], established in large-volume lattice simulations, both in SU(2) [29] and in SU(3) [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Renormalization group analysis of the gluon mass equation

2014

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In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, whose deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ans\"atze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive-definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.Comment: 33 pages, 11 figure

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“…The third application is the study of the conditions under which the (non-perturbative) Schwinger-Dyson (SD) equations can be reliably trusted when expanding around non-trivial vacua. As shown in [24] for some toy models, a naive SD expansion is poor when the potential admits more than one minimum; on the other hand, a modified SD formulation, is required in order to improve on the saddle point approximation in such cases. The formalism developed here and in [18] can indeed help in formulating the SD expansion in the presence of topologically non trivial vacuum configurations (instantons, center vortices, monopoles, etc.…”

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confidence: 99%

Background field method as a canonical transformation

Binosi

Quadri

2012

Phys. Rev. D

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We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.

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Schwinger-Dyson equations and disorder

Cited by 5 publications

References 41 publications

Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

Renormalization group analysis of the gluon mass equation

Background field method as a canonical transformation

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