HAMILTONIAN BFV-BRST THEORY OF CLOSED QUANTUM COSMOLOGICAL MODELS

We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models, The f ull set of constraints is split into area-preserving spatial diffeomor phisms, forming closed subalgebra, and Virasoro-like generators. Opera tional Hamiltonian BFV-BRST quantization is performed in the framework of perturbative expansion in the dimensionless parameter, which is a positive power of the ratio of Planckian volume to the volume of the U niverse. For the (N + 1)-dimensional generalization of stationary clos ed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a ce rtain relationship between the dimensionality of the space and the spe ctrum of matter fields emerges from the requirement of quantum consist ency of the model. (C) 1997 Elsevier Science B.V.