Aharonov-Bohm Problem for Spin-One

TL;DR

This paper investigates the Aharonov-Bohm effect for spin-1 particles, revealing how magnetic flux influences particle behavior, bound states, and vacuum currents, with implications for nonrelativistic regimes.

Contribution

It extends the Aharonov-Bohm problem to spin-1 particles, analyzing bound states, vacuum currents, and the conditions for nonrelativistic regimes.

Findings

Particles generally do not penetrate the flux tube at most flux values.

Bound states move freely along the tube axis below a certain energy threshold.

Vacuum currents induced by the flux supplement rather than screen the magnetic flux.

Abstract

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