  We prove the existence of the dynamics automorphism group for Hamiltonian QCD
on an infinite lattice in R^3, and this is done in a C*-algebraic context. The
existence of ground states is also obtained. Starting with the finite lattice
model for Hamiltonian QCD developed by Kijowski & Rudolph, we state its field
algebra and a natural representation. We then generalize this representation to
the infinite lattice, and construct a Hilbert space which has represented on it
all the local algebras (i.e. kinematics algebras associated with finite
connected sublattices) equipped with the correct graded commutation relations.
On a suitably large C*-algebra acting on this Hilbert space, and containing all
the local algebras, we prove that there is a one parameter automorphism group,
which is the pointwise norm limit of the local time evolutions along a sequence
of finite sublattices, increasing to the full lattice. This is our global time
evolution. We then take as our field algebra the C*-algebra generated by all
the orbits of the local algebras w.r.t. the global time evolution. Thus the
time evolution creates the field algebra. The time evolution is strongly
continuous on this choice of field algebra, though not on the original larger
C*-algebra. We define the gauge transformations, explain how to enforce the
Gauss law constraint, show that the dynamics automorphism group descends to the
algebra of physical observables and prove that gauge invariant ground states
exist.
