### 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.

Original language | English (US) |
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Pages (from-to) | 73-90 |

Number of pages | 18 |

Journal | Few-Body Systems |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2010 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Few-Body Systems*,

*47*(1), 73-90. https://doi.org/10.1007/s00601-009-0073-0