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Journal of Modern Physics

The Relativistic Time-Dependent Aharonov-Bohm Effect

A. Petridis, Zachary Kertzman, Khinlay Win

Published Jan 1, 2014• 0 citations
Publisher

Abstract

The relativistic Aharonov-Bohm (AB) effect is studied using the time-dependent Dirac equation. It is shown that if the initial electron distribution is a pulse it is possible to define time-dependent signals that distinguish the AB effect from dipole and induced Coulomb interactions.
DOI
10.4236/jmp.2014.516164

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The Aharonov-Bohm effect is considered by most authors as a quantum effect, but a generally accepted explanation does not seem to be available. The phenomenon is studied here under the assumption that hypothetical electric dipole distributions configured by moving charges in the solenoid act on the electrons as test particles. The relative motions of the interacting charged particles introduce relativistic time dilations. The massless dipoles are postulated as part of an impact model that has recently been proposed to account for the far-reaching electrostatic forces between charged particles described by Coulomb's law. The model provides a quantitative explanation of the Aharonov-Bohm effect.
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Exact analytic solutions are found to the Dirac equation in 2+12+12+1 dimensions for a combination of an Aharonov-Bohm potential and the Lorentz three-vector and scalar Coulomb potentials. By means of the solutions obtained the relativistic quantum Aharonov-Bohm effect is studied for the free (in the presence of a Lorentz three-vector Coulomb potential) and bound fermion states. We obtain the total scattering amplitude in a combination of the Aharonov-Bohm and Lorentz three-vector Coulomb potentials as a sum of two scattering amplitudes. This modifies the expression for the standard Aharonov-Bohm cross section due to the interference of these two amplitudes with each other. We discuss that the observable quantities can be the phases of electron wave functions or the energies of bound states.