A variational method from the variance of energy

Siringo, Fabio; Marotta, L.

doi:10.1140/epjc/s2005-02358-x

Cited by 32 publications

(56 citation statements)

References 19 publications

(22 reference statements)

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“…The method of stationary variance [10,11] is a second order variational technique that is suited to describe gauge theories with a minimal coupling like gauge theories [29,30], where first order approximations like the GEP do not add anything to the standard treatment of perturbation theory [27]. The method has been discussed in some detail in Ref.…”

Section: Setup Of the Methodsmentioning

confidence: 99%

“…In this paper we test the method of stationary variance [10,11] that has been shown to be viable in simple Abelian gauge theories like QED [30]. According, the self-energy graphs are required up to second order, since the equation for stationary variance can be derived by the general connection that has been proven in Ref.…”

Section: Setup Of the Methodsmentioning

confidence: 99%

“…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]. The GEP is a genuine variational method and has been successfully applied to many physical problems in field theory, from scalar and electroweak theories [15][16][17][18][19][20][21][22] to superconductivity [23][24][25] and antiferromagnetism [26], but turns out to be useless for gauge interacting fermions [27].…”

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: Setup Of the Methodsmentioning

confidence: 99%

Section: Setup Of the Methodsmentioning

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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“…In fact the GEP always predicts a weak first order transition at the critical point even for the neutral superfluid (real scalar theory) [30]. This is not a problem for the interpolation of the experimatal data as the difference only arises in a very narrow range of temperature at the transition point.…”

Section: Interpolation Of the Experimental Datamentioning

confidence: 97%

General interpolation scheme for thermal fluctuations in superconductors

et al. 2006

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We present a general interpolation theory for the phenomenological effects of thermal fluctuations in superconductors. Fluctuations are described by a simple gauge invariant extension of the gaussian effective potential for the Ginzburg-Landau static model. The approach is shown to be a genuine variational method, and to be stationary for infinitesimal gauge variations around the Landau gauge. Correlation and penetration lengths are shown to depart from the mean field behaviour in a more or less wide range of temperature below the critical regime, depending on the class of material considered. The method is quite general and yields a very good interpolation of the experimental data for very different materials.

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“…That is a consequence of the one-loop approximation, since if all higher-order terms were included the result would not depend on m. Actually, at one-loop, if the dressing functions are multiplied by an arbitrary factor Z = 1 + α δZ ≈ 1, that factor should be compensated by the subtraction of αδZ on the right-hand sides of Eqs. (26). Thus an only partial degree of compensation reflects a sensitivity to the choice of the scale m. On the other hand, the one-loop approximation can be optimized by taking additive constants that minimize the effects of higher orders.…”

Section: Pure Yang-mills Theorymentioning

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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A variational method from the variance of energy

Cited by 32 publications

References 19 publications

Gluon propagator in Feynman gauge by the method of stationary variance

Gluon propagator in Feynman gauge by the method of stationary variance

General interpolation scheme for thermal fluctuations in superconductors

Analytic structure of QCD propagators in Minkowski space

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