Aharonov-Bohm Effect Based on the Huygens Principle

Akira Tonomura

Kiyoshi Kawamura, Y. Zempo, Y. Irie

The Aharonov-Bohm (AB) equation is reformulated by means of the gauge transformation. A scattering theoretical approach yields an integral equation of the form of Kirchhoff-Huygens. The method to solve this equation is analogous to the one previously used to study the dislocation mediated AB effect. It is reconfirmed that the shadow of the magnetic-flux filament appears in the down stream of the electronic flux. Expression for the large angle scattering obtained by AB is improved and the present expression is shown to agree with numerical solution.

Alexander V. Gritsunov, Natalie Masolova

The locality principle fulfillment in the Aharonov-Bohm (AB) effect is analyzed from the point of view of a self-sufficient potential formalism based on so-called gradient hypothesis in electrodynamics. The "magnetic" kind of AB effect is examined (as the quantum charged particle moves to an infinitely long solenoid with a permanent current), and no locality principle violation recognized if the gradient hypothesis is used. A conclusion is made that AB effect is no longer a physical and electrodynamic "paradox".

Murray Peshkin

Alexander V. Gritsunov

Two hypotheses concerning the Lagrange function postulating for a system with electromagnetic interactions: (classic) and (new) are compared. It is shown that the gradient hypothesis, unlike the vortex one, does not result in conflict between the Aharonov-Bohm (AB) effect and the locality principle. A modification of AB effect in Zero Magnetic (ZM) oscillation of potential around excited closed waveguide is predicted.

Benjamin Liebowitz