The manifestly covariant Aharonov-Bohm effect in terms of the 4D fields

TL;DR

This paper presents a covariant formulation of the Aharonov-Bohm effect using 4D geometric quantities, revealing the role of electric fields outside a stationary solenoid in the phase difference.

Contribution

It introduces a manifestly covariant 4D geometric approach to the AB effect, emphasizing the electric field's influence over the vector potential.

Findings

Electric field exists outside a stationary resistive solenoid.

The AB phase can be determined by the electric component of the 4D fields.

The electric field influences the AB phase without nonzero vector potential.

Abstract

In this paper it is presented a manifestly covariant formulation of the Aharonov-Bohm (AB) phase difference for the magnetic AB effect . This covariant AB phase is written in terms of the Faraday 2-form F and using the decomposition of F in terms of the electric and magnetic fields as four-dimensional (4D) geometric quantities. It is shown that there is a static electric field outside a stationary solenoid with resistive conductor carrying steady current, which causes that the AB phase difference in the magnetic AB effect may be determined by the electric part of the covariant expression, i.e. by the local influence of the 4D electric field and not, as generally accepted,in terms of nonzero vector potential.