JNR Monopoles

TL;DR

This paper reviews the theory of JNR hyperbolic monopoles, focusing on their spectral curves and rational maps, and presents new formulas for energy density and conditions for spectral curves.

Contribution

It establishes conditions for spectral curves of JNR monopoles and derives a simple form for the holomorphic sphere, linking scattering results to monopole properties.

Findings

Spectral curve conditions for JNR monopoles

A simple formula for the energy density at infinity

Examples illustrating energy-density distribution

Abstract

We review the theory of JNR, mass 1/2 hyperbolic monopoles in particular their spectral curves and rational maps. These are used to establish conditions for a spectral curve to be the spectral curve of a JNR monopole and to show that that rational map of a JNR monopole monopole arises by scattering using results of Atiyah. We show that for JNR monopoles the holomorphic sphere has a remarkably simple form and show that this can be used to give a formula for the energy density at infinity. In conclusion we illustrate some examples of the energy-density at infinity of JNR monopoles.