  In order to determine the origin of discontinuities which arise when the
semiclassical propagator is employed to describe an infinitely long and
infinitesimally thin solenoid carrying magnetic flux, we give a systematic
derivation of the semiclassical limit of the motion of an otherwise free
charged particle. Our limit establishes the connection of the quantum
mechanical canonical angular momentum to its classical counterpart. Moreover,
we show how a picture of Aharonov-Bohm interference of two half-waves acquiring
Dirac's magnetic phase when passing on either side of the solenoid emerges from
the quantum propagator, and that the typical scale of the resulting
interference pattern is fully determined by the ratio of the angular part of
Hamilton's principal function to Planck's constant. The semiclassical
propagator is recovered in the limit when this ratio diverges. We discuss the
relation of our results to the whirling-wave representation of the exact
propagator.
