The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States

Abstract

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We briefly discuss the issues of gauge fixing, BRS invariance and positivity. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. The influence of instantons on DSEs in a 2-dimensional model is mentioned. Solutions for the Green's functions in QED in 2+1 and 3+1 dimensions provide tests of various schemes to truncate DSEs. We discuss possible extensions to QCD and their limitations. Truncation schemes for DSEs of QCD are discussed in the axial gauge and in the Landau gauge. We review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. The applications of QCD Green's functions to hadron physics are summarized. Properties of ground state mesons are discussed on the basis of the Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and mechanisms of diquark confinement are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark-diquark correlations in the quantum field theory of confined quarks and gluons.Comment: 212 Pages, LaTeX2e, submitted to Physics Reports; typos corrected, improvements on grammar and style, references adde