  We construct a set of states that implement the non-Abelian Gauss's law for
QCD. We also construct a set of gauge-invariant operator-valued quark and gluon
fields by establishing an explicit unitary equivalence between the Gauss's law
operator and the `pure glue' part of the Gauss's law operator. This unitary
equivalence enables us to use the `pure glue' Gauss's law operator to represent
the entire Gauss's law operator in a new representation. Since the quark field
commutes with the `pure glue' Gauss's law operator, it is a gauge-invariant
field in this new representation. We use the unitary equivalence of the new and
the conventional representations to construct gauge-invariant quark and gluon
fields in both representations, and to transform the QCD Hamiltonian in the
temporal gauge so that it is expressed entirely in terms of gauge-invariant
quantities. In that form, all interactions between quark fields mediated by
`pure gauge' components of the gluon field have been transformed away, and
replaced by a nonlocal interaction between gauge-invariant color-charge
densities. This feature --- that, in gauge-invariant formulations, interactions
mediated by pure gauge components of gauge fields have been replaced by
nonlocal interactions --- is shared by many gauge theories. In QED, the
resulting nonlocal interaction is the Coulomb interaction, which is the Abelian
analog of the QCD interaction we have identified and are describing in this
work. The leading term, in a multipole expansion, of this nonlocal QCD
interaction vanishes for quarks in color-singlet configurations, suggesting a
dynamical origin for color confinement; higher order terms of this multipole
expansion suggest a QCD mechanism for color transparency. We also show how, in
an SU(2) model, this nonlocal interaction can be evaluated nonperturbatively.
