Covariant factor ordering of gauge systems using ghost variables. II. States and observables

The aim of any constraint quantization procedure is to be able to recover the physical content of a system after quantizing on the extended state space (which will include both physical and unphysical configurations). Within the Dirac approach to such problems there is no guarantee that the resulting quantum theory will be equivalent to the quantized physical theory and one has to be content with a case by case analysis of its applicability. In this paper it is shown that for finite-dimensional systems with first class constraints linear in momenta, invariance under constraint rescaling and point transformations is sufficient to ensure a consistent quantization. As discussed in the preceding paper [J. Math. Phys. 30, XXX (1989)], in order to become a manifest symmetry, constraint rescaling requires ghost variables. It is now shown how the associated BRST charge is constructed and how it is used to describe the physical states and observables in the constrained system. The extension of this construction to more general constrained systems is also discussed