A Simple Proof of Magnetic and Electric Aharonov-Bohm Effects

TL;DR

This paper presents new, simplified proofs of both magnetic and electric Aharonov-Bohm effects, including the first proof of the electric effect in domains with moving boundaries, avoiding complex existing theories.

Contribution

It provides novel, simplified proofs of the magnetic and electric Aharonov-Bohm effects, notably addressing the electric effect in dynamic boundary domains for the first time.

Findings

New proof of magnetic AB effect without scattering theory

First proof of electric AB effect in domains with moving boundaries

Electric AB effect absent when boundaries are static

Abstract

Magnetic Aharonov-Bohm effect (AB effect) was studied in hundreds of papers starting with the seminal paper of Aharonov and Bohm [AB] published in 1959. We give a new proof of the magnetic Aharonov-Bohm effect without using the scattering theory and the theory of inverse boundary value problems. We consider separately the cases of one and several obstacles. The electric AB effect was studied much less. We give the first proof of the electric AB effect in domains with moving boundaries. When the boundary does not move with the time the electric AB effect is absent.