Modern Approaches to Non-Perturbative QCD and Other Confining Gauge Theories

Abstract

The primary goal of this Special Issue was to create a collection of reviews on the modern approaches to the problem of quark confinement in QCD [...]

Graph polynomials associated with Dyson-Schwinger equations

“…However these formal expansions can be governed by perturbation methods in weakly coupled physical theories with vanishing beta function. In other words, Dyson-Schwinger equations behave linearly in the conformal part of the physical theory while in non-conformal part, these equations behave non-linearly [1,4,20,26,27,38].…”

“…Solutions of these quantum motions are given by polynomials with respect to c g such that the appropriate higher loop order Feynman diagrams are coefficients in these expansions. The analysis of these solutions at energies < Λ QCD encapsulates low energy QCD, where running coupling constants increase and non-perturbative aspects such as confinement do happen [1,4,19,32,33,35,38,39]. Firstly, graph polynomials are useful tools for the study of Feynman integrals which contribute to the structure of 1PI Green's functions [2,3,9,21,22].…”