Second-order effects of the magnetic vector potential in the Aharonov-Bohm experiment

TL;DR

This paper explores second-order effects of the magnetic vector potential in the Aharonov-Bohm experiment, revealing a displacement force and conservation of angular momentum, consistent with experimental observations.

Contribution

It introduces a second-order expansion of the magnetic vector potential to explain lateral displacements and force effects in the Aharonov-Bohm experiment, enhancing theoretical understanding.

Findings

Identification of a displacement force due to second-order vector potential effects

Conservation of canonical angular momentum in the system

Consistency with experimental results including fringe shifts and lateral displacements

Abstract

Recent experiments with the Aharonov-Bohm geometry have shown that, in addition to an electron-interference fringe shift, there is also a lateral displacement of the electron diffraction envelope. In this paper, we derive a displacement force based on a second-order expansion of the magnetic vector potential. The analysis illustrates the conservation of canonical angular momentum, where the mechanical angular momentum and field angular momentum sum to a constant of the motion; the azimuthal force required to change the mechanical momentum is thus supplied by changes in field momentum associated with the second-order vector potential term. Our results are consistent with all known Aharonov-Bohm experiments, including interference fringe shifts, lateral displacement forces, and the absence of longitudinal forces.