Magnetic Flux, Angular Momentum, and Statistics

Abstract

It is demonstrated that the orbital angular momentum ${l}_{z}$ of a particle of charge $q$ orbiting around a tube with magnetic flux $\ensuremath{\Phi}$ is quantized in units ${l}_{z}=\mathrm{integer}\ensuremath{-}\frac{q\ensuremath{\Phi}}{2\ensuremath{\pi}}$. A very simple physical argument for this is presented, and applied to understand the Dirac quantization condition and the charge-spin relation for particles bound to magnetic monopoles. The unusual statistics of flux-tube-charged-particle composites is discussed.