Magnetic force exerted by the Aharonov-Bohm line

Abstract

The controversial question of the transverse force exerted by the Aharonov-Bohm (AB) magnetic flux line is reconsidered with the help of a new paraxial solution to the AB-scattering problem. It is shown that despite the left-right symmetry in the AB scattering cross-section, a beam of a finite width is deflected by the AB-line as if by the ``Lorentz'' force. The asymmetry and the magnetic force originate from the quantum interference in the forward direction within the angular size of the incident wave. In the context of the superfluid He-4 theory, the paper confirmes the Iordanskii force acting on the vortex line.