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Von Neumann's Quantization of General Relativity | | A.B. Arbuzov
; A.Yu. Cherny
; D.J. Cirilo-Lombardo
; R.G. Nazmitdinov
; Nguyen Suan Han
; A.E. Pavlov
; V.N. Pervushin
; A.F. Zakharov
; | | Date: |
11 Nov 2015 | | Abstract: | 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, 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 Noether theorem) and the
initial data transformations (as objects of the first Noether 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. | | Source: | arXiv, 1511.3396 | | Services: | Forum | Review | PDF | Favorites | |
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