Covariant variational approach to Yang-Mills theory

Quandt, Markus; Reinhardt, Hugo; Heffner, Jan

doi:10.1103/physrevd.89.065037

Cited by 51 publications

(83 citation statements)

References 75 publications

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“…In the present context the technique turns out to be equivalent to the expansion proposed by Reinhardt and Feuchter [5] and recently used in the Lagrangian formalism in Ref. [8]. In more detail, the first untrivial term of the expansion is the quadratic one, yielding the correction δS I…”

Section: Comparison With Other Variational Methodsmentioning

confidence: 90%

“…In Coulomb gauge [4][5][6][7]9] and in Landau gauge [8,[31][32][33][34][35][36][37][38][39] there has been an intense theoretical work in the last years. In Landau gauge theoretical and lattice data are generally explained in terms of a decoupling regime, with a finite ghost dressing function and a finite massive gluon propagator.…”

Section: Introductionmentioning

confidence: 99%

“…The IR slavery of these theories makes the standard perturbation theory useless below some energy scale, and our theoretical knowledge of the IR limit relies on lattice simulation and on non-perturbative techniques like functional renormalization group [1] and Dyson-Schwinger equations [2]. Variational methods have been developed as a complement to these analytical approaches, and their utility has been proven by several authors in the last years [3][4][5][6][7][8][9]. Quite recently, the method of stationary variance [10,11] has been advocated as a powerful second order extension of the Gaaussian Effective Potential (GEP) [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Gluon propagator in Feynman gauge by the method of stationary variance

Siringo

2014

Phys. Rev. D

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The low-energy limit of pure Yang-Mills SU (3) gauge theory is studied in Feynman gauge by the method of stationary variance, a genuine second-order variational method that is suited to deal with the minimal coupling of fermions in gauge theories. In terms of standard irreducible graphs, the stationary equations are written as a set of coupled non-linear integral equations for the gluon and ghost propagators. A physically sensible solution is found for any strength of the coupling. The gluon propagator is finite in the infrared, with a dynamical mass that decreases as a power at high energies. At variance with some recent findings in Feynman gauge, the ghost dressing function does not vanish in the infrared limit and a decoupling scenario emerges as recently reported for the Landau gauge.

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Section: Comparison With Other Variational Methodsmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gluon propagator in Feynman gauge by the method of stationary variance

Siringo

2014

Phys. Rev. D

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“…Most of the non-perturbative approaches that have been developed so far rely on numerical calculations in the Euclidean space, where synergic studies by lattice simulations [2][3][4][5][6][7][8][9][10], Schwinger-Dyson equations [11][12][13][14][15][16][17][18][19][20][21] and variational methods [22][23][24][25][26][27][28][29][30][31][32] have drawn a clear picture for the propagators of QCD deep in the IR.…”

Section: Introductionmentioning

confidence: 99%

Analytic structure of QCD propagators in Minkowski space

Siringo

2016

Phys. Rev. D

105

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Analytical functions for the propagators of QCD, including a set of chiral quarks, are derived by a one-loop massive expansion in the Landau gauge, deep in the infrared. By analytic continuation, the spectral functions are studied in Minkowski space, yielding a direct proof of positivity violation and confinement from first principles.The dynamical breaking of chiral symmetry is described on the same footing of gluon mass generation, providing a unified picture. While dealing with the exact Lagrangian, the expansion is based on massive free-particle propagators, is safe in the infrared and is equivalent to the standard perturbation theory in the UV. By dimensional regularization, all diverging mass terms cancel exactly without including mass counterterms that would spoil the gauge and chiral symmetry of the Lagrangian. Universal scaling properties are predicted for the inverse dressing functions and shown to be satisfied by the lattice data. Complex conjugated poles are found for the gluon propagator, in agreement with the i-particle scenario.

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“…In recent years, much effort has been devoted to develop nonperturbative continuum approaches. These are based on either Dyson-Schwinger equations [2][3][4][5][6][7] or functional renormalization group flow equations [8,9], or they exploit the variational principle in either the Hamiltonian [10,11] or covariant [12,13] formulation of gauge theory. There are also semiphenomenological approaches assuming a massive gluon propagator [14] or the Gribov-Zwanziger action [15]; see [16].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

Reinhardt

Burgio

Campagnari

et al. 2018

Advances in High Energy Physics

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We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang-Mills theory, the deconfinement phase transition is found to be second order for SU(2) and first order for SU(3), in agreement with the lattice results. The corresponding critical temperatures are found to be 275 MeV and 280 MeV, respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of 198 MeV and 170 MeV, respectively, for the deconfinement and chiral transition.

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Covariant variational approach to Yang-Mills theory

Cited by 51 publications

References 75 publications

Gluon propagator in Feynman gauge by the method of stationary variance

Gluon propagator in Feynman gauge by the method of stationary variance

Analytic structure of QCD propagators in Minkowski space

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

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