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FINITE-GAP INTEGRATION OF THE SU(2) BOGOMOLNY EQUATIONS

Published online by Cambridge University Press:  01 February 2009

H. W. BRADEN  and
V. Z. ENOLSKI
H. W. BRADEN
Affiliation:
School of Mathematics, Edinburgh University, Edinburgh e-mail: hwb@ed.ac.uk
V. Z. ENOLSKI
Affiliation:
Institute of Magnetism, National Academy of Sciences of Ukraine, Ukraine e-mail: vze@ma.hw.ac.uk
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Abstract

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The Atiyah–Drinfeld–Hitchin–Manin–Nahm (ADHMN) construction of magnetic monopoles is given in terms of the (normalizable) solutions of an associated Weyl equation. We focus here on solving this equation directly by algebro-geometric means. The (adjoint) Weyl equation is solved using an ansatz of Nahm in terms of Baker–Akhiezer functions. The solution of Nahm's equation is not directly used in our development.

Keywords

35Q5814H7037J35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue A , February 2009 , pp. 25 - 41
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Braden, H. W. and Enolski, V., Remarks on the complex geometry of 3-monopole (2006), 1–65, arXiv: math-ph/0601040.Google Scholar
2.Dubrovin, B. A., Completely integrable systems related to matrix operators and abelian varieties, Funk. Anal. Appl. 11 (4) (1977), 28–41.Google Scholar
3.Ercolani, N. and Sinha, A., Monopoles and Baker functions, Commun. Math. Phys. 125 (1989), 385–416.CrossRefGoogle Scholar
4.Hitchin, N. J., Monopoles and Geodesics, Commun. Math. Phys. 83 (1982), 579–602.CrossRefGoogle Scholar
5.Hitchin, N. J., On the Construction of Monopoles, Commun. Math. Phys. 89 (1983), 145–190.CrossRefGoogle Scholar
6.Nahm, W., The construction of all self-dual multimonopoles by the ADHM method (World Scientific, Singapore, 1982).Google Scholar
7.Panagopoulos, H., Multimonopoles in arbitrary gauge groups and the complete su(2) two-monopole system, Phys. Rev. D 28 (2) (1983), 380–384.CrossRefGoogle Scholar
8.Weinberg, E. J. and Piljin, Yi, Magnetic monopole dynamics, supersymmetry and duality, Phys. Rep. 438 (2007), 65–236, arXiv: hep-th/0609055.CrossRefGoogle Scholar