  We present a new reformulation of the canonical quantum geometrodynamics,
which allows to overcome the fundamental problem of the frozen formalism and,
therefore, to construct an appropriate Hilbert space associate to the solution
of the restated dynamics. More precisely, to remove the ambiguity contained in
the Wheeler-DeWitt approach, with respect to the possibility of a (3 +
1)-splitting when the space-time is in a quantum regime, we fix the reference
frame (i.e. the lapse function and the shift vector) by introducing the
so-called kinematical action; as a consequence the new super-Hamiltonian
constraint becomes a parabolic one and we arrive to a Schroedinger-like
approach for the quantum dynamics. In the semiclassical limit our theory
provides General Relativity in the presence of an additional energy-momentum
density contribution coming from no longer zero eigenvalues of the Hamiltonian
constraints; the interpretation of these new contributions comes out in natural
way as soon as it is recognized that the kinematical action can be recasted in
such a way it describes a pressureless, but, in general, non geodesic perfect
fluid.
