  The quantum mechanically admissible definitions of the factor
$\exp\big[(i/\hbar)S(\gamma)\big]$ 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.
