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 full set of constraints is splitted into area-preserving spatial diffeomorphisms, forming closed subalgebra, and Virasoro-like generators. Operatorial 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 Universe. For the (N+1) - dimensional generalization of stationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out, that certain relationship between dimensionality of the space and the spectrum of matter fields emerges from the requirement of quantum consistency of the model. 
A.Yu. Kamenshchik and S.L. Lyakhovich (International Centre for   Theoretical Physics, Trieste, Italy)