Communications in Mathematical Physics

, Volume 89, Issue 2, pp 145–190

On the construction of monopoles

  • N. J. Hitchin

DOI: 10.1007/BF01211826

Cite this article as:
Hitchin, N.J. Commun.Math. Phys. (1983) 89: 145. doi:10.1007/BF01211826


We show that any self-dual SU (2) monopole may be constructed either by Ward's twistor method, or Nahm's use of the ADHM construction. The common factor in both approaches is an algebraic curve whose Jacobian is used to linearize the non-linear ordinary differential equations which arise in Nahm's method. We derive the non-singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions.

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • N. J. Hitchin
    • 1
  1. 1.St. Catherine's CollegeOxfordEngland

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