Shear of the vector potential in the Aharonov-Bohm effect

TL;DR

This paper investigates a shear component of the vector potential in the Aharonov-Bohm effect, revealing a local, velocity-dependent interaction that explains various experimental observations without relying on local electric or magnetic fields.

Contribution

It introduces a novel shear component of the vector potential, offering a new perspective on the geometric phase and local interactions in the AB effect.

Findings

Shear field provides a velocity-dependent phase interaction.

Predictions align with interference fringe shifts and no time delays.

Lateral forces are possible within this framework.

Abstract

The Aharonov-Bohm (AB) effect is now largely considered to be a manifestation of geometric phase. However, by decomposing the vector-potential gradient tensor into divergence, curl, and shear components, we isolate a field/charged-particle interaction that is not dependent on local electric and magnetic fields. We show that a local shear field provides a velocity-dependent, dynamic-phase interaction in the AB effect whose predictions are consistent with all known classes of AB experiments, including interference fringe shifts, the absence of time delays along the direction of propagation, and the possibility of lateral forces.