Green's Functions for Composite Particles in Quantum Chromodynamics

Abstract

We discuss the bound state problem of quantum chromodynamics. We give the reduc­ tion formula for nonlocal gauge-invariant composite operators which describe composite particles using the method of Haag, Nishijima and Zimmermann. We develop the method of auxiliary fields for nonlocal gauge-invariant composite operators. § 1. Introduction Different models of strong interactions have been proposed corresponding to different energy regions considered; that is, current algebra and chiral dynamics for the low energy region; the dual resonance model and the dual string model for the Regge energy region; and the parton model for the deep inelastic region. Recently, quantum chromodynamics (QCD) has attracted much interest of particle physicists as a model which may combine properties of the models of three energy regions. Quarks are probably confined; at least, they have not appeared in the experi­ ments up to the present. Therefore the ordinary perturbative expansion with quarks and gluons as intermediate states may not reveal the real physical world, because the ordinary perturbation theory restricts asymptotic conditions. The ex­ pansions must probably be carried out using bound states of quarks and gluons as intermediate states. Moreover, the Regge pole theory and the dual model indicate that not only stable hadrons but also unstable resonances should be included in the intermediate states, while the dual string model suggests that the intermediate states have semiclassical string configurations. Further, only the states which can be described by color singlet states have been observed and no massless particles participating in strong interactions seem to exist. These facts suggest that the color gauge invariance remains unbroken even by the state vectors and the asymptotic states are gauge-invarianel, 2J (see also Ref.