Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory

Details Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory

2009-05-28

arxiv.org/abs/0905.4594v1

Few Body Syst.47:73-90,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

22 pages, 4 figures, 1 table

Scientific paper

10.1007/s00601-009-0073-0

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.

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