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In order to determine the origin of discontinuities which arise when thesemiclassical propagator is employed to describe an infinitely long andinfinitesimally thin solenoid carrying magnetic flux, we give a systematicderivation of the semiclassical limit of the motion of an otherwise freecharged particle. Our limit establishes the connection of the quantummechanical canonical angular momentum to its classical counterpart. Moreover,we show how a picture of Aharonov-Bohm interference of two half-waves acquiringDirac's magnetic phase when passing on either side of the solenoid emerges fromthe quantum propagator, and that the typical scale of the resultinginterference pattern is fully determined by the ratio of the angular part ofHamilton's principal function to Planck's constant. The semiclassicalpropagator is recovered in the limit when this ratio diverges. We discuss therelation of our results to the whirling-wave representation of the exactpropagator.

Semiclassical asymptotics of the Aharonov-Bohm interference process