Geodesic
Three-dimensional volume of a~closed universe as a~canonical time parameter
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 541-548

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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. 
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     author = {N. N. Gorobey and A. S. Lukyanenko},
     title = {Three-dimensional volume of a~closed universe as a~canonical time parameter},
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N. N. Gorobey; A. S. Lukyanenko. Three-dimensional volume of a~closed universe as a~canonical time parameter. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 541-548. http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a9/