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We examine a nonlocal interaction that results from expressing the QCDHamiltonian entirely in terms of gauge-invariant quark and gluon fields. Theinteraction couples one quark color-charge density to another, much as electriccharge densities are coupled to each other by the Coulomb interaction in QED.In QCD, this nonlocal interaction also couples quark color-charge densities togluonic color. We show how the leading part of the interaction between quarkcolor-charge densities vanishes when the participating quarks are in a colorsinglet configuration, and that, for singlet configurations, the residualinteraction weakens as the size of a packet of quarks shrinks. Because of thiseffect, color-singlet packets of quarks should experience final stateinteractions that increase in strength as these packets expand in size. For thecase of an SU(2) model of QCD based on the {\em ansatz} that thegauge-invariant gauge field is a hedgehog configuration, we show how theinfinite series that represents the nonlocal interaction between quarkcolor-charge densities can be evaluated nonperturbatively, without expanding itterm-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.Comment: Revtex, 23 pages; contains additional references with brief comments  on sam

QUARK CONFINEMENT AND COLOR TRANSPARENCY IN A GAUGE-INVARIANT FORMULATION OF QCD