A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge
Abstract
A truncation scheme for the Dyson-Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov-Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling alpha_c of approx. 9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations.
Keywords
Cite
@article{arxiv.hep-ph/9707327,
title = {A Solution to Coupled Dyson-Schwinger Equations for Gluons and Ghosts in Landau Gauge},
author = {Lorenz von Smekal and Andreas Hauck and Reinhard Alkofer},
journal= {arXiv preprint arXiv:hep-ph/9707327},
year = {2009}
}
Comments
60 pages, LaTeX209, 17 figures (epsfig.sty), to appear in Ann. Phys., some typos corrected. In particular, in Eqs. (83), (85) and (90) a factor 1/(4 kappa) that was erroneously inserted in the original typing process had to be removed. We are indebted to A. Cucchieri for helping us become aware of this typo