Von Neumann's procedure is applied for quantization of General Relativity. We
quantize the initial data of dynamical variables at the Planck epoch, where the
Hubble parameter coincides with the Planck mass. These initial data are defined
via the Fock simplex in the tangent Minkowskian space-time and the Dirac
conformal interval. The Einstein cosmological principle is applied for the
average of the spatial metric determinant logarithm over the spatial volume of
the visible Universe. We derive the splitting of the general coordinate
transformations into the diffeomorphisms (as the object of the second N\"other
theorem) and the initial data transformations (as objects of the first N\"other
theorem). Following von Neumann, we suppose that the vacuum state is a quantum
ensemble. The vacuum state is degenerated with respect to quantum numbers of
non-vacuum states with the distribution function that yields the Casimir effect
in gravidynamics in analogy to the one in electrodynamics. The generation
functional of the perturbation theory in gravidynamics is given as a solution
of the quantum energy constraint. We discuss the region of applicability of
gravidynamics and its possible predictions for explanation of the modern
observational and experimental data.Comment: 14 pages, updated version with extended discussio
