  The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a
representation in which it is expressed entirely in terms of gauge-invariant
quark and gluon fields. In a subspace of gauge-invariant states we have
constructed that implement the non-Abelian Gauss's law, this unitarily
transformed Weyl-gauge Hamiltonian can be further transformed and, under
appropriate circumstances, can be identified with the QCD Hamiltonian in the
Coulomb gauge. To circumvent the problem that this Hamiltonian, which is
expressed entirely in terms of gauge-invariant variables, must be used with
nonnormalizable complicated states that implement the non-Abelian Gauss's law,
we demonstrate an isomorphism that materially facilitates the application of
this Hamiltonian to a variety of physical processes, including the evaluation
of $S$-matrix elements. This isomorphism relates the gauge-invariant
representation of the Hamiltonian and the required set of gauge-invariant
states to a Hamiltonian of the same functional form but dependent on ordinary
unconstrained Weyl-gauge fields operating within a space of `standard'
perturbative states. The fact that the gauge-invariant chromoelectric field is
not hermitian has important implications for the functional form of the
Hamiltonian finally obtained. When this nonhermiticity is taken into account,
the `extra' perturbative terms in Christ and Lee's Coulomb-gauge Hamiltonian
are natural outgrowths of the formalism. When this nonhermiticity is neglected,
the Hamiltonian used in the earlier work of Gribov and others results.
