Constraints and polarizations

Geometric quantization is applied to first-class constrained systems. It is shown how certain inconsistencies associated with the prequantization of open gauge algebras and observables can be cured at the quantum level by the introduction of suitable polarizations. Furthermore it is shown how a large Poisson subalgebra of the ideal of constraint functions can be consistently implemented at the quantum level and how reparametrization invariance of the constraint surface relates to a partially flat local Kaehler structure on phase space. (orig.)