Von Neumann's quantization of general relativity

Abstract

Von Neumann's procedure is applied for quantization of General Relativity.We quantize the initial data ofdynamical 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 Diracconformal interval. The Einstein cosmological principle is applied for the average of the spatial metricdeterminant logarithm over the spatial volume of the visible Universe.We derive the splitting of the general coordinate transformations into the diffeomorphisms and the initial data transformations. 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 (excited) states. It has a distribution function that yields the Casimir effect in gravidynamics in analogy to the one in electrodynamics. The generation functionalof the perturbation theory in gravidynamics is given as a solution of the quantum energy constraint. Wediscuss the region of applicability of gravidynamics and its possible predictions for explanation of themodern observational and experimental data.