OPERATOR ORDERING IN THEORIES SUBJECT TO CONSTRAINTS OF THE GRAVITATIONAL TYPE

Covariant operator realization of Dirac constraints is proposed in the ories of the gravitational type, subject to Hamiltonian and momentum c onstraints. This realization is based on their metric and Killing conf iguration-space structures, has Hermitian conjugation properties follo wing from the BFV quantization method and generalizes to the level of the exact theory (apart from the problem of the ultraviolet regulariza tion and anomalies) the recently proposed semiclassical algorithms in models with arbitrary first-class constraints.