ON THE IMPLICATIONS OF CONFINEMENT

We consider some implications of confinement starting from the basic observation that cross-sections for the production of colored asymptotic states, such as free quarks and gluons, from color singlet initial states must be zero if QCD is to be confining. We discuss two pictures of confinement: the failure of the cluster decomposition property and the absence of a pole at timelike momenta in the propagator of a confined particle. We use QCD-based models as a framework to relate the failure of the cluster decomposition property to other ideas, such as the role of a nonzero gluon condensate. Our primary interest is to address the question of the absence of a mass pole through a study of model Schwinger-Dyson equations. These equations contain some of the dynamical information that is present in the study of the cluster decomposition property. We discuss the problems with this idea and its study using the Schwinger-Dyson equations.