Path-integral representation of the wave function: The relativistic particle

The path-integral representation for the wave function of a relativistic particle is studied as a model of parametrized theories. We construct the transition amplitude by means of a phase-space path integral and discuss some problems coming from the ambiguity in a gauge-fixing procedure. The explicit calculation in the canonical gauge reveals the discrepancy in the procedure of Batalin, Fradkin, and Vilkovisky as to the ambiguity of whether one has to adopt the Faddeev-Popov determinant or the absolute value of it.