Four approaches to quantization of the relativistic particle

Abstract

The connection between four different approaches to quantization of the relativistic particle is studied: reduced phase space quantization, Dirac quantization, BRST quantization, and (BRST)-Fock quantization are each carried out. The connection to the BFV path integral in phase space is provided. In particular, it is concluded that that the full range of the lapse should be used in such path integrals. The relationship between all these approaches is established.