Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole

TL;DR

This paper analyzes the non-relativistic scattering of a spin-1/2 particle by a self-dual monopole, revealing that at large distances it simplifies to a known dyon problem and that the total cross-section remains unchanged by spin.

Contribution

It demonstrates that the scattering problem reduces to a previously studied dyon case and shows the S matrix factorizes into spinless and spin-dependent parts, with identical total cross-section.

Findings

S matrix factorizes into spinless and spin-dependent components

Total cross-section matches the spinless case

Scattering reduces to the dyon problem at large distances

Abstract

The non-relativistic scattering of a spin-1/2 particle off a self-dual monopole reduces, for large distances, to the dyon problem, studied previously by D'Hoker and Vinet. The S matrix (calculated by Zwanziger's algebraic method based on the o(3,1)\oplus o(3) dynamical symmetry, discovered by D'Hoker and Vinet) is shown to factorize into the product of the spinless S-matrix, S_0, with a spin-dependent factor. The total cross-section is identical to the one found in the spinless case.