  This work concerns a new reformulation of quantum geometrodynamics, which
allows to overcome a fundamental ambiguity contained in the canonical approach
to quantum gravity: the possibility of performing a (3+1)-slicing of
space-time, when the metric tensor is in a quantum regime. Our formulation
provides also a procedure to solve the problems connected to the so called
"frozen formalism". In particular 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 hamiltonian constraints become parabolic, so
arriving to evolutive (Schroedinger-like) equations for the quantum dynamics.
The kinematical action can be interpreted as the action of a pressureless, but,
in general, non geodesic perfect fluid, so in the semi classical limit our
theory leads to the dynamics of the gravitational field coupled to a dust which
represents the material reference frame we have introduced fixing the slicing.
We also investigate the cosmological implications of the presence of the dust,
which, in the WKB limit of a cosmological problem, makes account for a "dark
matter" component and could play, at present time, a dynamical role.
