Prequantisation from the path integral viewpoint

Abstract

The quantum mechanically admissible definitions of the factor $\exp [(i/\hslash )S({\hat{I}}^3)]$ in the Feynman integral are put in bijection with the prequantisations of Kostant and Souriau. The different allowed expressions of this factor -- the inequivalent prequantisations -- are classified. The theory is illustrated by the Aharonov-Bohm experiment and by identical particles.

Slightly reworded, rearranged and extended version of one originally published in the Proceedings of the {\sl Int. Conf. on Diff. Geom. Meths. in Math. Phys.}, Clausthal'1980, Doebner (ed). Springer Lecture Notes in Math. \textbf{905}, p.197-206 (1982). Marseille preprint CPT-80-P-1230. 14 pages, 2 figures