Path Integrals in a Multiply-Connected Configuration Space (50 Years After)

The proposal made 50 years ago by Schulman (1968), Laidlaw & Morette-DeWitt (1971) and Dowker (1972) to decompose the propagator according homotopy classes of paths was a major breakthrough: it showed how Feynman functional integrals opened direct window on quantum properties topological origin in configuration space. This paper casts critical look at arguments brought this series papers its numerous followers an attempt clarify reason why emergence unitary linear representation first group is not only sufficient but also necessary.