Prequantisation from the path integral viewpoint

The quantum mechanically admissible definitions of the factor $\exp [(i\mathrm{/}\mathrm{\hslash })S(\gamma )]$ 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.