Operator representation of gravitational constraints in the case of a closed universe

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.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 503–507, December, 1995.