The principle of stationary variance is advocated as a viable variational approach to gauge theories. The method can be regarded as a second-order extension of the Gaussian Effective Potential (GEP) and seems to be suited for describing the strong-coupling limit of non-Abelian gauge theories. The single variational parameter of the GEP is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of coupled integral equations. The stationary conditions can be easily derived by the self-energy, without having to write the effective potential, making use of a general relation between self-energy and functional derivatives that has been proven to any order. The low-energy limit of pure Yang-Mills SU(3) gauge theory has been studied in Feynman gauge, and the stationary equations are written as 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.

Variational Study of SU(3) Gauge Theory by Stationary Variance

SIRINGO, Fabio
2015-01-01

Abstract

The principle of stationary variance is advocated as a viable variational approach to gauge theories. The method can be regarded as a second-order extension of the Gaussian Effective Potential (GEP) and seems to be suited for describing the strong-coupling limit of non-Abelian gauge theories. The single variational parameter of the GEP is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the solution of a set of coupled integral equations. The stationary conditions can be easily derived by the self-energy, without having to write the effective potential, making use of a general relation between self-energy and functional derivatives that has been proven to any order. The low-energy limit of pure Yang-Mills SU(3) gauge theory has been studied in Feynman gauge, and the stationary equations are written as 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.
2015
DYNAMICAL MASS GENERATION, HIGGS SECTOR, SUPERCONDUCTIVITY, MODEL.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/41937
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