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Physics of Particles and Nuclei

The Aharonov–Bohm Effect: an Algebraic Approach

D. A. Slavnov

Published Jan 1, 2019• 1 citation
Publisher

Abstract

Abstract An algebraic approach to the Aharonov–Bohm effect is considered. The constructed mathematical scheme agrees with experimental data and provides a clear physical interpretation of this effect that does not contradict classical concepts.
DOI
10.1134/s1063779619010040

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Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.
The independence of the Aharonov-Bohm phase shift on particle velocity is one of its defining properties. The classical counterpart to this dispersionless behavior is the absence of forces along the direction of motion of the particle. A reevaluation of the experimental demonstration that forces are absent in the AB physical system is given, including previously unpublished data. It is shown that the debate on the presence or absence of forces is not settled, and an experiment searching for dispersionless forces is proposed.