Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect

TL;DR

This paper explores how the breaking of a global symmetry to a discrete subgroup can produce Aharonov-Bohm-like effects, with specific analysis of scattering phenomena involving vortices and particles.

Contribution

It demonstrates the emergence of Aharonov-Bohm analogues from symmetry breaking and analyzes scattering effects at low momentum in this context.

Findings

Low-momentum scattering cross-section approaches Aharonov-Bohm limit

Effect diminishes at high momentum

Spin-1/2 particle scattering off magnetic vortex as an experimental example

Abstract

It is shown that the breakdown of a {\it global} symmetry group to a discrete subgroup can lead to analogues of the Aharonov-Bohm effect. At sufficiently low momentum, the cross-section for scattering of a particle with nontrivial $\Z_2$ charge off a global vortex is almost equal to (but definitely different from) maximal Aharonov-Bohm scattering; the effect goes away at large momentum. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realizable example.