  An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of
Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is
constructed in the continuum. This operator is entirely free of factor ordering
singularities and can be defined in symmetric and non-symmetric form. We work
in the real connection representation and obtain a well-defined quantum theory.
We compute the complete solution to the Quantum Einstein Equations for the
non-symmetric version of the operator and a physical inner product thereon. The
action of the Wheeler-DeWitt constraint on spin-network states is by
annihilating, creating and rerouting the quanta of angular momentum associated
with the edges of the underlying graph while the ADM-energy is essentially
diagonalized by the spin-network states. We argue that the spin-network
representation is the ``non-linear Fock representation" of quantum gravity,
thus justifying the term ``Quantum Spin Dynamics (QSD)".

General Relativity and Quantum Cosmology;High Energy Physics - Theory