Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9702100 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Aharonov-Bohm problem for spin 1

M. L. Horner, Alfred S. Goldhaber

Published May 15, 1997• 3 citations
arXivHTMLPDF

Abstract

The basic AB problem is to determine how an unshielded tube of magnetic flux $\ensuremath{\Phi}$ affects arbitrarily long-wavelength charged particles impinging on it. For spin 1 at almost all $\ensuremath{\Phi}$ the particles do not penetrate the tube, so the interaction essentially is periodic in $\ensuremath{\Phi}$ (AB effect). Below-threshold bound states move freely only along the tube axis, and consequent induced vacuum currents supplement rather than screen $\ensuremath{\Phi}$. For a pure magnetic interaction the tube must be broader than the particle Compton wavelength, i.e., only the nonrelativistic spin-$1$ AB problem exists.

DOI
10.1103/physrevd.55.5951

Related papers

Gauge-independent description of the Aharonov-Bohm effect

Xiang Li, T. H. Hansson, Wei Ku

The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region inaccessible to the particle. Classically, such a nonlocal effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schr\"odinger equation, has a local coupling between the current due to the particle and the electromagnetic vector potential $\mathbf{A}$, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics $\mathbf{A}$ is in some sense more ``fundamental'' than $\mathbf{B}$ in spite of the former being gauge dependent and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB effect can be fully accounted for by considering only the gauge-invariant $\mathbf{B}$ field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge-invariant formulation is that we must give up locality---the AB phase for the particle will arise from the change in the action for the $\mathbf{B}$ field in the region inaccessible to the particle.

arXiv:2209.11091•Physical Review A•Sep 21, 2022•9 citations

Relativistic Aharonov–Bohm–Coulomb Problem

C. R. Hägen, D. K. Park

The ((2+1)-dimensional) Aharonov–Bohm effect is analyzed for a spin-1/2 particle in the case that a 1/rpotential is present. Scalar and vector couplings are each considered. It is found that the approach in which the flux tube is given a finite radius that is taken to zero only after a matching of boundary conditions does not give physically meaningful results. Specifically, the operations of taking the limit of zero flux tube radius and the Galilean limit do not commute. Thus there appears to be no satisfactory solution of the relativistic Aharonov–Bohm–Coulomb problem using the finite radius flux tube method.

arXiv:hep-th/9410225•Annals of Physics•Oct 1, 1996•32 citations

Boundary conditions in the Aharonov-Bohm effect for particles with spin

Sergey A. Voropaev, Michael Bordag B

Unknow•Jan 1, 1993•0 citations

THE AHARONOV-CASHER EFFECT

In 1984, 25 years after the prediction of the →Aharonov-Bohm (AB) effect, Aharonov and Casher [1] predicted a “dual ” effect. In both effects, a particle is excluded from a tubular region of space, but otherwise no force acts on it. Yet it acquires a measurable quantum phase that depends on what is inside the tube of space from which it is excluded. In the AB effect, the particle is charged and the tube contains a magnetic flux. In the Aharonov-Casher (AC) effect, the particle is neutral, but has a magnetic moment, and the tube contains a line of charge. Experiments in neutron [2], vortex [3], atom [4], and electron [5] interferometry bear out the prediction of Aharonov and Casher. Here we briefly explain the logic of the AC effect and how it is dual to the AB effect. We begin with a two-dimensional version of the AB effect. Figure 1 shows an electron moving in a plane, and also a “fluxon”, i.e. a small region of magnetic flux (pointing out of the plane) from which the electron is excluded. In Fig. 1 the fluxon is in a quantum superposition of two positions, and the electron diffracts around one of the positions but not the other. Initially, the fluxon and electron are in a

•Nov 26, 2012•0 citations

The role of boundary conditions in the Aharonov-Bohm effect for particles with spin

Sergey A. Voropaev, Michael Bordag B

Journal of Experimental and Theoretical Physics•Feb 1, 1994•3 citations

The Aharonov–Bohm effect in scattering of short-wavelength particles

Yu. A. Sitenko, N.D. Vlasii

Quantum-mechanical scattering of nonrelativistic charged particles by a magnetic vortex of nonzero transverse size is considered. We show that the flux of the vortex serves as a gate for the strictly forward propagation of particles with short, as compared to the transverse size of the vortex, wavelengths; this effect is the same for a penetrable vortex as for an impenetrable one. A possibility for the experimental detection of the scattering Aharonov–Bohm effect is discussed.

arXiv:1111.5937•Journal of Physics A Mathematical and Theoretical•Mar 20, 2012•1 citation
The basic AB problem is to determine how an unshielded tube of magnetic flux \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ affects arbitrarily long-wavelength charged particles impinging on it. For spin 1 at almost all \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ the particles do not penetrate the tube, so the interaction essentially is periodic in \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ (AB effect). Below-threshold bound states move freely only along the tube axis, and consequent induced vacuum currents supplement rather than screen \ensuremathΦ\ensuremath{\Phi}\ensuremathΦ. For a pure magnetic interaction the tube must be broader than the particle Compton wavelength, i.e., only the nonrelativistic spin-111 AB problem exists.
The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle that encircles a magnetic flux located in a region inaccessible to the particle. Classically, such a nonlocal effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle. In quantum mechanics, the Hamiltonian, and thus the Schr\"odinger equation, has a local coupling between the current due to the particle and the electromagnetic vector potential A\mathbf{A}A, which extends to the entire space beyond the region with finite magnetic field. This has sometimes been interpreted as meaning that in quantum mechanics A\mathbf{A}A is in some sense more ``fundamental'' than B\mathbf{B}B in spite of the former being gauge dependent and thus unobservable. Here we shall, with a general proof followed by a few examples, demonstrate that the AB effect can be fully accounted for by considering only the gauge-invariant B\mathbf{B}B field, as long as it is included as part of the quantum action of the entire isolated system. The price for the gauge-invariant formulation is that we must give up locality---the AB phase for the particle will arise from the change in the action for the B\mathbf{B}B field in the region inaccessible to the particle.
The ((2+1)-dimensional) Aharonov–Bohm effect is analyzed for a spin-1/2 particle in the case that a 1/rpotential is present. Scalar and vector couplings are each considered. It is found that the approach in which the flux tube is given a finite radius that is taken to zero only after a matching of boundary conditions does not give physically meaningful results. Specifically, the operations of taking the limit of zero flux tube radius and the Galilean limit do not commute. Thus there appears to be no satisfactory solution of the relativistic Aharonov–Bohm–Coulomb problem using the finite radius flux tube method.
In 1984, 25 years after the prediction of the →Aharonov-Bohm (AB) effect, Aharonov and Casher [1] predicted a “dual ” effect. In both effects, a particle is excluded from a tubular region of space, but otherwise no force acts on it. Yet it acquires a measurable quantum phase that depends on what is inside the tube of space from which it is excluded. In the AB effect, the particle is charged and the tube contains a magnetic flux. In the Aharonov-Casher (AC) effect, the particle is neutral, but has a magnetic moment, and the tube contains a line of charge. Experiments in neutron [2], vortex [3], atom [4], and electron [5] interferometry bear out the prediction of Aharonov and Casher. Here we briefly explain the logic of the AC effect and how it is dual to the AB effect. We begin with a two-dimensional version of the AB effect. Figure 1 shows an electron moving in a plane, and also a “fluxon”, i.e. a small region of magnetic flux (pointing out of the plane) from which the electron is excluded. In Fig. 1 the fluxon is in a quantum superposition of two positions, and the electron diffracts around one of the positions but not the other. Initially, the fluxon and electron are in a