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Solving a Coupled Set of Truncated QCD Dyson–Schwinger Equations (1998)
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BibTeX
@MISC{Hauck98solvinga,
author = {A. Hauck and L. von Smekal and R. Alkofer},
title = { Solving a Coupled Set of Truncated QCD Dyson–Schwinger Equations},
year = {1998}
}
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Abstract
Truncated Dyson–Schwinger equations represent finite subsets of the equations of motion for Green’s functions. Solutions to these non–linear integral equations can account for non–perturbative correlations. A closed set of coupled Dyson–Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4–point correlations and by implementing the Slavnov–Taylor identities for the 3–point vertex functions. We solve this coupled set in an one–dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson–Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previoulsy neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the non–perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, αc ≃ 9.5.
Keyphrases
coupled set truncated qcd dyson schwinger equation fau tp3 unitu thep non perturbative subtraction scheme non perturbative correlation ghost propagator gluon propagator finite subset point correlation small spacelike momentum coupled dyson schwinger equation slavnov taylor identity critical value dimensional approximation green function stable result non linear integral equation closed set gluon dyson schwinger equation integral equation previous solution mandelstam approximation dyson schwinger equation landau gauge qcd analytic infrared expansion point vertex function
