Studies of confinement: How the gluon propagates

The behavior of the gluon propagator in the Landau gauge is studied over distances from the scales probed in deep-inelastic scattering out to the size of a hadron: from the perturbative to the nonperturbative regimes: using the Schwinger-Dyson equations. The approximations needed to make the program tractable are both detailed and analyzed by considering two different calculational schemes, one of which takes into account more fully the complete structure of the crucial triple-gluon vertex. In both cases, the gluon propagator is found to be strongly enhanced like 1/p4 at low momenta p. We describe how this depends on Λ, the scale of QCD dynamics, and what this behavior means for the confinement potential. The use of a covariant gauge avoids difficulties inherent in axial gauges, where much previous work has been done, the differences with which are discussed