2010/05/11 by Markus Q. Huber, Huber, Markus Q.
Physics and Astronomy · #Quantum Chromodynamics and Particle Interactions #Cold Atom Physics and Bose-Einstein Condensates #High-Energy Particle Collisions Research
paper · pdf · doi:10.48550/arxiv.1005.1775
The infrared behavior of propagators and vertices is derived for the\nmaximally Abelian gauge and the Gribov-Zwanziger action relying on functional\nequations. The derivation and analysis of Dyson-Schwinger equations increase\nconsiderably in complexity when going beyond the standard Landau gauge fixing\nand the available tools have to be improved. For the derivation of the\nequations a computer program (DoDSE) was developed in order to handle the\nplethora of terms. The process of determining possible infrared solutions is\nabstracted to obtain further insight into the structure of the so-called\ninfrared scaling solutions. It is found that a few simple steps suffice to\ndetermine possible infrared scaling relations directly from the action. For the\nmaximally Abelian gauge an infrared enhanced diagonal gluon propagator is\nfound, while the off-diagonal degrees of freedom are infrared suppressed. This\nis in agreement with the idea of Abelian infrared dominance. Furthermore, it is\nproven that SU(2) and higher SU(N) have the same infrared behavior, although\nthe corresponding actions differ. Under a suitable truncation the\nDyson-Schwinger equations are solved in the deep infrared to obtain values for\nthe exponents of the power laws. Restricting the integration in field\nconfiguration space to the Gribov region of the Landau gauge with the\nGribov-Zwanziger action leads to two qualitatively equivalent infrared\nsolutions. In both cases the gluon propagator is infrared suppressed and the\ninfrared enhanced ghost propagator dominates the Dyson-Schwinger equations.\nThis result corroborates the conjecture by Zwanziger that the functional\nintegration can be cut at the first Gribov horizon and only the applied\nboundary conditions are important. For one solution the Dyson-Schwinger\nequations reduce in the deep infrared exactly to those obtained with the usual\nFaddeev-Popov gauge fixing.\n