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Truncating First-Order Dyson–Schwinger Equations in Coulomb Gauge Yang–Mills Theory

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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.

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Authors and Affiliations

  1. Institute for Physics, Karl-Franzens University, Graz, Universitätsplatz 5, 8010, Graz, Austria

    Reinhard Alkofer & Axel Maas

  2. New York University, New York, NY, 10003, USA

    Daniel Zwanziger

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  1. Reinhard Alkofer
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  2. Axel Maas
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  3. Daniel Zwanziger
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Correspondence to Axel Maas.

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Alkofer, R., Maas, A. & Zwanziger, D. Truncating First-Order Dyson–Schwinger Equations in Coulomb Gauge Yang–Mills Theory. Few-Body Syst 47, 73–90 (2010). https://doi.org/10.1007/s00601-009-0073-0

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