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arXiv · 2509.26533

Topology of the Aharonov-Bohm effect in different reference frames

Hiram S. M. Rodrigues·Katson W. O. Arévola·Pablo L. Saldanha
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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.

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Hiram S. M. Rodrigues, Katson W. O. Arévola, Pablo L. Saldanha. 2025-09-30. Topology of the Aharonov-Bohm effect in different reference frames. https://doi.org/10.1103/r1ht-zspf

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