Operator representation of gravitational constraints for the case of the closed universe

N. N. Gorobey^a, A. S. Lukyanenko

^a State Technological Institute of St. Petersburg

Abstract: The Witten identity is used to obtain a representation of gravitational constraints for a closed Universe as an equality of two operators in the space of Dirac bispinors, the Dirac operator squared and the Laplace operator. Degeneracy of the spectra of these operators represents the Lorentz invariance of the Hamiltonian dynamics of the Universe in special gauges connected with the new operator representation.

Received: 13.01.1995

 English version: Theoretical and Mathematical Physics, 1995, 105:3, 1603–1606

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