PhotonIcs and Electromagnetics Research Symposium,
also known as Progress In Electromagnetics Research Symposium
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Published by The Electromagnetics Academy
Published: 2015-08-28
Aharonov-Bohm Effect, Poincare Lemma and Gauge Invariance
By
Alexander F. Klinskikh,
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    Alexander F. Klinskikh

    Voronezh State University, Russia

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Peter A. Meleshenko,
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    Peter A. Meleshenko

    Voronezh State University, Russia

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Hang T. T. Nguyen,
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    Hang T. T. Nguyen

    Vietnam National University, Vietnam

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Mikhail E. Semenov
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    Mikhail E. Semenov

    Zhukovsky-Gagarin Air Force Academy, Russia

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Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)740-743
Abstract
In this paper we demonstrate the peculiarities of the Aharonov-Bohm effect using the theory of generalized functions. We show that the presence of the Aharonov-Bohm effect violates the Poincaré lemma (in other words the Poincaré lemma does not apply to the Aharonov- Bohm spatial geometry), moreover, such a violation is a necessary condition for the Aharonov- Bohm effect observation. The unexpected form of the Schrödinger equation for the Aharonov- Bohm effect which contains a singularity in explicit form is also obtained. These results allow to take a fresh look on the Aharonov-Bohm problem.
Citation
Alexander F. Klinskikh, Peter A. Meleshenko, Hang T. T. Nguyen, and Mikhail E. Semenov, "Aharonov-Bohm Effect, Poincare Lemma and Gauge Invariance," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9，Page(s)740-743
References

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