Aharonov-Bohm effect, local field interaction, and Lorentz invariance

TL;DR

This paper introduces a Lorentz-invariant local field interaction framework for the Aharonov-Bohm effect, eliminating potentials and resolving fundamental interpretational issues.

Contribution

A novel local field interaction scheme for the Aharonov-Bohm effect that is fully consistent with relativity and removes the need for potentials.

Findings

Resolves duality issues with Aharonov-Casher effect

Eliminates potentials in the description of the effect

Provides a Lorentz-covariant local interaction model

Abstract

A field-interaction scheme is introduced for describing the Aharonov-Bohm effect, fully consistent with the principle of relativity. Our theory is based on the fact that local field interactions are present even when a particle moves only in a field-free region. The interaction Lagrangian between a charge and a flux is uniquely constructed from three principles: Lorentz covariance, linearity in the interaction strength, and a correct stationary limit of charge. Our result resolves fundamental questions raised on the standard interpretation of the Aharonov-Bohm effect, concerning its duality with the Aharonov-Casher effect and the equivalence between the potential and the field-interaction models for describing the electromagnetic interaction. Most of all, potential is eliminated in our theory, and all kind of the force-free Aharonov-Bohm effect is understood in a unified framework of the Lorentz-covariant local interaction of electromagnetic fields.