Communications in Mathematical Physics

, Volume 96, Issue 3, pp 387–407

Nahm's equations and the classification of monopoles

  • S. K. Donaldson


Solutions of Nahm's system of ordinary differential equations are produced by variational methods. This leads to an explicit parametrisation of the solutions to the Bogomolny equation over ℝ3.


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  1. 1.
    Atiyah, M. F.: Instantons in two and four dimensions. Commun. Math. Phys.93, 437–451 (1984)Google Scholar
  2. 2.
    Atiyah, M. F., Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. R. Soc. London308, 523–615 (1982)Google Scholar
  3. 3.
    Donaldson, S. K.: Anti self dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles. Proc. Lond. Math. Soc.50, 1–26 (1985)Google Scholar
  4. 4.
    Donaldson, S. K.: Instantons and geometric invariant theory. Commun. Math. Phys.93, 453–460 (1984)Google Scholar
  5. 5.
    Hitchin, N. J.: Monopoles and geodesics. Commun. Math. Phys.83, 579–602 (1982)Google Scholar
  6. 6.
    Hitchin, N. J.: On the construction of monopoles. Commun. Math. Phys.89, 145–190 (1983)Google Scholar
  7. 7.
    Hurtubise, J. C.: SU(2) monopoles of charge 2. Commun. Math. Phys.92, 195–202 (1983)Google Scholar
  8. 8.
    Jaffe, A., Taubes, C. H.: Vortices and monopoles. Boston: Birkhäuser 1980Google Scholar
  9. 9.
    Kempf, G., Ness, L.: On the lengths of vectors in representation spaces. In: Lecture Notes in Mathematics, Vol.372, Berlin, Heidelberg, New York: Springer, 1978Google Scholar
  10. 10.
    Murray, M. K.: Monopoles and spectral curves for arbitrary Lie Groups. Commun. Math. Phys.90, 263–271 (1983)Google Scholar
  11. 11.
    Murray, M. K.: D. Philos. Thesis, Oxford (1983)Google Scholar
  12. 12.
    Nahm, W.: All self dual multimonopoles for arbitrary gauge group. (Preprint) TH 3172-CERN (1981)Google Scholar
  13. 13.
    Nahm, W.: The algebraic geometry of multimonopoles. Preprint, Physikalisches Institut, University of BonnGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • S. K. Donaldson
    • 1
    • 2
  1. 1.All Souls CollegeOxfordUnited Kingdom
  2. 2.The Institute for Advanced StudyPrincetonUSA

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