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

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

Jun 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993tmp....95..766g&link_type=abstract

Theoretical and Mathematical Physics, Volume 95, Issue 3, pp.766-770

Mathematics

Mathematical Physics

Scientific paper

The dynamics of a spatially closed universe is studied in gravitation theory by means of the eigenfunctions and eigenvalues of the 3 D projection of the Dirac operator. In a gauge that we call the Ashtekar gauge and construct by using an eigenfunction of this operator, the 3 D 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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