Physical projections in BRST treatments of reparametrization invariant theories (Q2746649)

In the present paper the authors perform a BRST quantization of a reparametrization invariant theory and reparametrization invariance is viewed as a gauge invariance. The detailed analysis of this BRST quantization is based on a precise operator formulation on inner product spaces. The relation to ordinary quantum mechanics, which is much more involved than in the Dirac quantization, is also explicitly demonstrated. It is shown in detail how time appears from the reparametrization invariant version. Finally the general formulas for how physical wave functions and propagators are to be projected from the BRST singlets and propagators in the ghost extended BRST theory are proposed.