The infrared behaviour 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 discuss the definition of the generating functional in gauge theories, in particular, the rôle of redundant degrees of freedom, possibilities of a complete gauge fixing versus gauge fixing in presence of Gribov copies, BRS invariance and positivity. The apparent contradiction between positivity and colour antiscreening in combination with BRS invariance in QCD is considered. 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 DysonSchwinger equations (DSEs) of QED and QCD. For the latter, the implications of BRS invariance on the Green's functions are explored. The possible influence of instantons on DSEs is discussed in a twodimensional model. In QED in (2+1) and (3+1) dimensions, the solutions for Green's functions provide tests of truncation schemes which can under certain circumstances be extended to the DSEs of QCD. We discuss some limitations of such extensions and assess the validity of assumptions for QCD as motivated from studies in QED. Truncation schemes for DSEs are discussed in axial and related gauges, as well as in the Landau gauge. Furthermore, we review the available results from a systematic nonperturbative 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 summarised. Properties of ground state mesons are discussed on the basis of the ladder BetheSalpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and a mechanism for diquark confinement beyond the ladder approximation are reviewed. We discuss some properties of ground state baryons based on their description as BetheSalpeter/Faddeev bound states of quarkdiquark correlations in the quantum field theory of confined quarks and gluons.
 Publication:

Physics Reports
 Pub Date:
 November 2001
 DOI:
 10.1016/S03701573(01)000102
 arXiv:
 arXiv:hepph/0007355
 Bibcode:
 2001PhR...353..281A
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 212 Pages, LaTeX2e, submitted to Physics Reports