This article is cited in 2 papers

Three-dimensional volume of a closed universe as a canonical time parameter

N. N. Gorobey, A. S. Lukyanenko

State Technological Institute of St. Petersburg

Abstract: The dynamics of a spatially closed universe is studied in gravitation theory by means of the eigenfunctions and eigenvalues of the $3D$ projection of the Dirac operator. In a gauge that we call the Ashtekar gauge and construct by using an eigenfunction of this operator, the $3D$ volume of a spatial section is a canonical parameter, and the energy is a positive-definite functional of the dynamical variables (on the region of the phase space in which $\dot V>0$) proportional to the corresponding eigenvalue. There is a discrete set of frames of reference distinguished in this manner.

Received: 26.03.1992

 English version: Theoretical and Mathematical Physics, 1993, 95:3, 766–770

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