The Charge 2 Monopole via the ADHMN construction

TL;DR

This paper applies integrable systems techniques to explicitly construct the charge 2 SU(2) Euclidean monopole using the ADHMN construction, solving a long-standing open problem and providing new analytic results.

Contribution

It provides the first explicit analytic formula for the charge 2 monopole via the ADHMN construction using integrable systems methods.

Findings

Explicit formulae for charge 2 monopole obtained

Comparison with previous results confirms correctness

New analytic expressions for monopole fields presented

Abstract

Recently we have shown how one may use use integrable systems techniques to implement the ADHMN construction and obtain general analytic formulae for the charge n su(2) Euclidean monopole. Here we do this for the case of charge 2: so answering an open problem of some 30 years standing. A comparison with known results and other approaches is made and new results presented.