  We present a separable version of Loop Quantum Gravity (LQG) based on an
inductive system of cubic lattices. We construct semi-classical states for
which the LQG operators -- the flux, the area and the volume operators -- have
the right classical limits. Also, we present the Hamilton and diffeomorphism
constraints as operator constraints and show that they have the right classical
limit. Finally, we speculate whether the continuum limit, which these
semi-classical states probe, can be defined for the entire construction and
thereby restore an action of the diffeomorphism group.
