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KUGO–OJIMA CONFINEMENT CRITERION, ZWANZIGER–GRIBOV HORIZON CONDITION, AND INFRARED CRITICAL EXPONENTS IN Landau Gauge QCD (2003)
BibTeX
@MISC{Alkofer03kugo–ojimaconfinement,
author = {R. Alkofer and C. S. Fischer and L. von Smekal},
title = { KUGO–OJIMA CONFINEMENT CRITERION, ZWANZIGER–GRIBOV HORIZON CONDITION, AND INFRARED CRITICAL EXPONENTS IN Landau Gauge QCD},
year = {2003}
}
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Abstract
The Kugo–Ojima confinement criterion and its relation to the infrared behaviour of the gluon and ghost propagators in Landau gauge QCD are reviewed. The realization of this confinement criterion (which in Landau gauge relates to Zwanziger’s horizon condition) results from quite general properties of the ghost Dyson– Schwinger equation. The numerical solutions for the gluon and ghost propagators obtained from a truncated set of Dyson–Schwinger equations provide an explicit example for the anticipated infrared behaviour. These results are in good agreement, also quantitatively, with corresponding lattice data obtained recently. The resulting running coupling approaches a fixed point in the infrared, α(0) = 8.9/Nc. Solutions for the coupled system of Dyson–Schwinger equations for the quark, gluon and ghost propagators are presented. Dynamical generation of quark masses and thus spontaneous breaking of chiral symmetry is found. In the quenched approximation the quark propagator functions agree well with those of corresponding lattice calculations. For a small number of light flavours the quark, gluon and ghost propagators deviate only slightly from the quenched ones. While the positivity violation of the gluon spectral function is apparent in the gluon propagator, there are no clear indications of positivity violations in the Landau gauge quark propagator.
Keyphrases
ghost propagator kugo ojima confinement criterion zwanziger gribov horizon condition infrared critical exponent positivity violation dyson schwinger equation landau gauge correct theory chiral symmetry good agreement clear indication gluon propagator hadronic reaction corresponding lattice data ghost dyson schwinger equation numerical solution quenched approximation general property quark mass quark propagator function perturbative qcd dynamical generation confinement criterion coupled system infrared behaviour landau gauge qcd gluon spectral function compelling evidence light flavour small number high energy truncated set gluon confinement anticipated infrared behaviour lattice calculation strong interaction spontaneous breaking horizon condition quenched one landau gauge quark propagator fixed point explicit example
