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 V > 0) proportional to the corresponding eigenvalue. There is a discrete set of frames of reference distinguished in this manner.
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Additional information
Leningrad State Technical University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 3, pp. 541–548, June, 1993.
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Gorobei, N.N., Luk'yanenko, A.S. Three-dimensional volume of a closed universe as a canonical time parameter. Theor Math Phys 95, 766–770 (1993). https://doi.org/10.1007/BF01017522
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DOI: https://doi.org/10.1007/BF01017522