  Any regular quantum mechanical system may be cast into an abelian gauge
theory by simply reformulating it as a reparametrization invariant theory. We
present a detailed study of the BRST quantization of such reparametrization
invariant theories within a precise operator version of BRST. The treatment
elucidates several intricate aspects of the BRST quantization of
reparametrization invariant theories like the appearance of physical time. We
propose general rules for how physical wave functions and physical propagators
are to be projected from the BRST singlets and propagators in the ghost
extended BRST theory. These projections are performed by boundary conditions
which are precisely specified by the operator BRST. We demonstrate explicitly
the validity of these rules for the considered class of models. The
corresponding path integrals are worked out explicitly and compared with the
conventional BFV path integral formulation.
