Infrared Behavior of QCD

Abstract

In this talk I will describe a series of calculations based on a general non-perturbative continuum approach to the problem of the IR behavior of QCO. This investigation, done in collaboration with F. Zachariasen and M. Baker, Is based on using the Schwinger-Dyson eqs. (hereafter S.D. eq.) for the quark and gluon propagators and using the appropriate Ward identities to obtain closed integral equations for the quantities of interest [1]. In particular, we have been able to show that a 1/q⁴ singularity in the gluon propagator produces a consistant solution to the integral equation. When this propagator is used in the integral equation for the quark propagator the pole singularity of a free massless quark is weakened to a simple square root branch point; furthermore we find that a mass-like tern (breaking chiral symmetry) which is an entire function, is consistent with the equations, though not required [2]. Finally, we construct an effective classical Lagrangian which is consistent with our form for the gluon propagator and automatically Includes the long range quantum fluctuations of QCD [3].