Constructing non-perturbative gauges using correlation functions

Gauge fixing in the non-perturbative domain of non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. To compare results from different methods it is necessary to resolve this ambiguity explicitly. Such a resolution is proposed using conditions on correlation functions for a family of non-perturbative Landau gauges. As a consequence, the various results available for correlation functions could possibly correspond to different non-perturbative Landau gauges, discriminated by an additional non-perturbative gauge parameter. The proposal, the necessary assumptions, and evidence from lattice gauge theory calculations, are presented in detail.Comment: in v2: Various modifications, discussion of results and scenario extended, references added in v3: Discussed definitions of what a Gribov ambiguity, a resolution of the ambiguity, and a Gribov problem is. Various minor improvement

Scalar-matter-gluon interaction

A full non-perturbative treatment of gauge theories requires to include matter fields on equal footing with the gauge fields. Scalar matter can act as a role model for generic matter, as many questions, e.g. confinement, can be posed without referring to a particular Lorentz structure. Due to their rather simple structure they are also useful to develop methods. One possible way to describe gauge theories beyond perturbation theory is based on correlation functions. After a short discussion of the setup, lattice gauge theory is used to analyze the interaction of gluons with quenched fundamental and adjoint scalars. Both the two-point and three-point correlation functions for massive and massless adjoint and fundamental scalars will be determined, in minimal Landau gauge. The findings are in agreement with the possibility that scalars are only slightly affected by the interaction with gluons. The results are compared briefly with dynamical, massive scalars, showing no significant changes in the confinement region compared to the quenched case.Comment: 10 pages, 3 figures, invited talk presented at the workshop "The many faces of QCD", Ghent, Belgium, 1st of November-5th of November 2010; submitted to the proceeding

Gauge engineering and propagators

Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.Comment: 9 pages, 4 figures, Conference: XIIth Quark Confinement and the Hadron Spectrum, August 28-September 04, 2016, Thessaloniki, Greece, submitted to the proceeding