A three-dimensional volume of the closed universe as a canonical time parameter.

Details A three-dimensional volume of the closed universe as a canonical time parameter. A three-dimensional volume of the closed universe as a canonical time parameter.

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993temf...95..541g&link_type=abstract

Teor. Mat. Fiz., Vol. 95, No. 3, p. 541 - 548

Mathematics

Logic

Cosmological Models: Gravitation Theory

Scientific paper

The dynamics of the spatially closed Universe in the theory of gravity is investigated by using eigenfunctions and eigenvalues of the spatial 3D-projection of the Dirac operator. In the Ashtekar gauge built by means of an eigenfunction of this operator the role of the time canonical parameter is played by the 3D-volume of the spatial section. The energy is an manifestly positively defined functional of dynamic variables (in the region of the phase space where V > 0) that is proportional to the corresponding eigenvalue. There is a discrete set of frames of reference distinguished in such a way.

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