Quark confinement and color transparency in a gauge-invariant formulation of QCD

We examine a nonlocal interaction that results from expressing the QCD Hami ltonian entirely in terms of gauge-invariant quark and gluon fields. The in teraction couples one quark color-charge density to another, much as electr ic charge densities are coupled to each other by the Coulomb interaction in QED. In QCD, this nonlocal interaction also couples quark color-charge den sities to gluonic color. We show how the leading part of the interaction be tween quark color-charge densities vanishes when the participating quarks a re in a color singlet configuration, and that, for singlet configurations, the residual interaction weakens as the size of a packet of quarks shrinks. Because of this effect, color-singlet packets of quarks should experience final state interactions that increase in strength as these packets expand in size. For the case of an SU(2) model of QCD based on the ansatz that the gauge-invariant gauge field is a hedgehog configuration, we show how the i nfinite series that represents the nonlocal interaction between quark color -charge densities can be evaluated nonperturbatively, without expanding it term-by-term. We discuss the implications of this model for QCD with SU(3) color and a gauge-invariant gauge field determined by QCD dynamics.