Aharonov-Bohm effect revisited

TL;DR

This paper reviews various types of the Aharonov-Bohm effect, discussing different approaches to prove its existence across quantum, electromagnetic, Yang-Mills, and gravitational contexts.

Contribution

It provides a comprehensive overview of methods used to demonstrate the Aharonov-Bohm effect in multiple physical and mathematical settings.

Findings

Different approaches to prove the AB effect are described

The paper covers magnetic, electric, electromagnetic, Yang-Mills, and gravitational AB effects

Various mathematical techniques like inverse problems and spectral analysis are discussed

Abstract

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 effect such as magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schr\"odinger 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.