Semiclassical Asymptotics of the Aharonov-Bohm Interference Process

We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov-Bohm interference of two half-waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling-wave representation of the exact propagator, and to previous approaches on the system's asymptotics.