Exact quantum description of the Aharonov–Bohm effect

The Aharonov–Bohm effect is considered in the fully quantum mechanical description, where the magnet as well as the moving charged particle is treated as a quantum object and interactions between them are mediated by virtual photon exchange. Employing the path integral representation, we not only establish the standard AB effect in an exact fashion but also reveal the origin of its topological nature for the proposed AB setup. In addition, complications arising from the transverse dispersion of the wave function of the charged particle and from the precession of the magnet are examined, and the conditions for the AB effect are discussed.