Abstract

The BRST Lagrangian approach of Kugo and Uehara (KU) is systematically used on phase space to obtain the canonical quantization of field theories with independent and linearly dependent first class constraints. The approach is most appropriate to discuss the boundary conditions under which the BFV theorem is valid. We obtain the minimal set of boundary conditions in terms of ghost fields. We carefully discuss the domain of integration for the BFV theorem for the relativistic particle and string theory.