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Abstract: The infrared behavior of propagators and vertices is derived for themaximally Abelian gauge and the Gribov-Zwanziger action relying on functionalequations. The derivation and analysis of Dyson-Schwinger equations increaseconsiderably in complexity when going beyond the standard Landau gauge fixingand the available tools have to be improved. For the derivation of theequations a computer program DoDSE was developed in order to handle theplethora of terms. The process of determining possible infrared solutions isabstracted to obtain further insight into the structure of the so-calledinfrared scaling solutions. It is found that a few simple steps suffice todetermine possible infrared scaling relations directly from the action. For themaximally Abelian gauge an infrared enhanced diagonal gluon propagator isfound, while the off-diagonal degrees of freedom are infrared suppressed. Thisis in agreement with the idea of Abelian infrared dominance. Furthermore, it isproven that SU2 and higher SUN have the same infrared behavior, althoughthe corresponding actions differ. Under a suitable truncation theDyson-Schwinger equations are solved in the deep infrared to obtain values forthe exponents of the power laws. Restricting the integration in fieldconfiguration space to the Gribov region of the Landau gauge with theGribov-Zwanziger action leads to two qualitatively equivalent infraredsolutions. In both cases the gluon propagator is infrared suppressed and theinfrared enhanced ghost propagator dominates the Dyson-Schwinger equations.This result corroborates the conjecture by Zwanziger that the functionalintegration can be cut at the first Gribov horizon and only the appliedboundary conditions are important. For one solution the Dyson-Schwingerequations reduce in the deep infrared exactly to those obtained with the usualFaddeev-Popov gauge fixing.

Autor: Markus Q. Huber

Fuente: https://arxiv.org/


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