On the infrared behaviour of QCD Green functions in the Maximally Abelian gauge

Abstract

Functional equations like exact renormalisation group and Dyson-Schwinger equations have contributed to a better understanding of non-perturbative phenomena in quantum field theories in terms of the underlying Green functions. In Yang-Mills theory especially the Landau gauge has been used, as it is the most accessible gauge for these methods. In the maximally Abelian gauge first results have been obtained which are very encouraging because Abelian infrared dominance has been found: The Abelian part of the gauge field propagator is enhanced at low momenta and thereby dominates the dynamics in the infrared. Also the ambiguity of two different types of solutions (decoupling and scaling) exists in both gauges. It is demonstrated how the two solutions are related in the maximally Abelian gauge. As in all two-point Dyson-Schwinger equations of the MAG the infrared dominant diagrams are sunset diagrams, in addition, a BPHZ regularisation and renormalisation of a test system with a sunset-like diagram is presented.

12 pages, 4 figures; Talk given at the International Workshop on QCD Green's Functions, Confinement and Phenomenology, 5-9 September 2011, Trento, Italy

References in corpus (13)

• Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations
• Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
• Chiral and deconfinement transition from Dyson-Schwinger equations
• The gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge: taking into account the effects of the Gribov copies and of the dimension two condensates
• CrasyDSE: A framework for solving Dyson-Schwinger equations
• Rho-meson, Bethe-Salpeter equation, and the far infrared
• Monopoles, abelian projection, and gauge invariance
• Non-perturbative analysis of the Gribov-Zwanziger action
• Linear Covariant Gauges on the Lattice
• Detecting monopoles on the lattice
• A study of the lightest glueball states in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge
• Infrared Propagators in MAG and Feynman gauge on the lattice
• Infrared scaling solutions beyond the Landau gauge: The maximally Abelian gauge and Abelian infrared dominance