Topology of the Aharonov-Bohm effect in different reference frames
Abstract
Recent works showed that the Aharonov-Bohm (AB) phase difference for a quantum charged particle can be written in terms of electric and magnetic fluxes in a spacetime surface whose boundaries are the possible particle worldlines in the interferometer, relative to the possible paths. After presenting this result in a more detailed way, reinforcing its topological nature, we study the magnetic and electric versions of the AB effect in different inertial reference frames. We find a particular reference frame for a magnetic AB effect where the magnetic flux has a null contribution for the AB phase difference, which is entirely due to an electric flux. Also, we find a particular reference frame for an electric AB effect where the electric flux has a null contribution for the AB phase difference, which is entirely due to a magnetic flux. In this sense, the nomenclatures 'magnetic AB effect' and 'electric AB effect' lose their meaning. We have electromagnetic AB effects.
Cite
@article{arxiv.2509.26533,
title = {Topology of the Aharonov-Bohm effect in different reference frames},
author = {Hiram S. M. Rodrigues and Katson W. O. Arévola and Pablo L. Saldanha},
journal= {arXiv preprint arXiv:2509.26533},
year = {2025}
}
Comments
7 pages, 6 figures