Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
Abstract
The non-perturbative domain of QCD contains confinement, chiral symmetry breaking, and the bound state spectrum. For the calculation of the latter, the Coulomb gauge is particularly well-suited. Access to these non-perturbative properties should be possible by means of the Green's functions. However, Coulomb gauge is also very involved, and thus hard to tackle. We introduce a novel BRST-type operator r, and show that the left-hand side of Gauss' law is r-exact. We investigate a possible truncation scheme of the Dyson-Schwinger equations in first-order formalism for the propagators based on an instantaneous approximation. We demonstrate that this is insufficient to obtain solutions with the expected property of a linear-rising Coulomb potential. We also show systematically that a class of possible vertex dressings does not change this result.
Keywords
Cite
@article{arxiv.0905.4594,
title = {Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory},
author = {Reinhard Alkofer and Axel Maas and Daniel Zwanziger},
journal= {arXiv preprint arXiv:0905.4594},
year = {2010}
}
Comments
22 pages, 4 figures, 1 table