Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 4

The charge $2$ monopole via the ADHMN construction

Pages: 791 – 956



H. W. Braden (School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, Scotland, United Kingdom)

V. Z. Enolski (National University of Kyiv-Mohyla Academy, Kyiv, Ukraine)


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 $2$ giving the first analytic expressions (for general $x \in \mathbb{R}^3$) for the gauge invariant $\mathrm{Tr} \Phi^2$, where $\Phi$ is the Higgs field, and the energy density. A comparison with known results and other approaches is made and new results presented.

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V. Z. Enolski died in 2019.

Appendix by David E. Braden, Peter Braden, and H. W. Braden

Published 12 April 2022