FOCK BUNDLES AND QUANTIZATION OF SYSTEMS WITH FIRST CLASS CONSTRAINTS

Abstract

The flat phase space (R2n, ω) with a symmetry group G generated by quadratic first class constraints is considered. We analyze the quantization of this constrained system in terms of the Fock bundle [Formula: see text], where S=Sp(2n, R)/U(n) is the space of positive translationally invariant complex structures J on (R2n, ω) and fibers HJ are the Hilbert spaces of quantization associated with the space (R2n, ω, J).