FOCK BUNDLES AND QUANTIZATION OF SYSTEMS WITH FIRST CLASS CONSTRAINTS

The flat phase space (R(2n),omega) with a symmetry group G generated b y quadratic first class constraints is considered. We analyze the quan tisation of this constrained system in terms of the Pock bundle H --> S, where S = Sp(2n,R)/U(n) is the space of positive translationally in variant complex structures J on (R(2n),omega) and fibers H-J are the H ilbert spaces of quantization associated with the space (R(2n),omega,J ).