On the problem concerning the Aharonov-Bohm effect

Dipankar Home, S. Sengupta

The controversy concerning theoretical treatment of the Aharonov–Bohm (AB) effect is critically investigated. A new approach, taking the time-dependent aspect of this effect into consideration, is proposed which seeks to resolve the prevalent ambiguities. This provides interesting insight into the origin of the AB effect. Some clarifications are also made regarding the experimental verification of this effect.

Daniel M. Greenberger

Herman Erlichson

The Aharonov-Bohm effect is relatively little known, but it poses fundamental questions in quantum theory. It concerns physical effects on charged particles in field-free regions. The present paper provides an over-all critical review and commentary on the literature of the Aharonov-Bohm effect. The two fundamental questions raised by the effect concern the role of the force concept in quantum mechanics, and the localizability of physical effects principle. A recent letter from Professor Bohm concerning his evaluation of the significance of the effect is included in the Appendix.

Heinz J. Rothe

Hans Boersch, K. Geohmann, H. Hamisch +2 more

Gregory Eskin

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.