Differential cross-sections and escape plots for low energy $SU(2)$ BPS magnetic monopole dynamics

TL;DR

This paper calculates classical scattering cross-sections for BPS $SU(2)$ magnetic monopoles, compares them with quantum results, and explores the classical dynamics and chaos in monopole and dyon interactions.

Contribution

It introduces a detailed numerical analysis of classical monopole scattering, revealing the topology of configuration space and chaotic dynamics, and compares classical and quantum cross-sections.

Findings

Classical and quantum BPS monopole cross-sections are closely approximated.

Quantum interference effects are numerically contradicted by classical results.

Classical monopole dynamics exhibit chaos and complex phase space structures.

Abstract

We compute the low-energy classical differential scattering cross-section for BPS $SU(2)$ magnetic monopoles using the geodesic approximation to the actual dynamics and 16K parallel processors on a CM2. Numerical experiments suggest that the quantum BPS magnetic monopole differential cross-section is well-approximated by the classical BPS magnetic monopole differential cross-section. In particular, the expected quantum interference effects for bosons at scattering angle $\theta=\pi/2$ (CoM frame) are contradicted numerically. We argue that this is due to the topology of the classical configuration space for these solitons. We also study the scattering and bounded classical motions of BPS dyons and their global structure in phase space by constructing `escape plots'. The escape plots contain a surprising amount of structure, and suggest that the classical dynamics of two BPS $SU(2)$ magnetic monopoles is chaotic and that there are closed and bounded two dyon motions with isolated energies.