Advertisement

Communications in Mathematical Physics

, Volume 90, Issue 2, pp 263–271 | Cite as

Monopoles and spectral curves for arbitrary Lie groups

  • M. K. Murray
Article

Abstract

The definition of the spectral curve of a monopole is extended to any connected, compact, simple Lie groupK. It is found there are rankK curves whose degrees are related to the topological weights of the monopole.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adams, J.F.: Lectures on Lie groups. New York, Amsterdam: Benjamin 1967Google Scholar
  2. 2.
    Atiyah, M.F.: Convexity and commuting Hamiltonians. Bull. London Math. Soc.14, 1–15 (1982)Google Scholar
  3. 3.
    Bernstein, I.N., Gel'fand, I.M., Gel'fand, S.I.: Schubert cells and cohomology of the spacesG/P. Russ. Math. Surv.28, 1–26 (1973)Google Scholar
  4. 4.
    Coddington, E.A., Levinson, N.: Theory of ordinary differential equations. New York, Toronto, London: McGraw-Hill 1955Google Scholar
  5. 5.
    Corrigan, E., Goddard, P.: Ann-monopole solution with 4n-1 degrees of freedom. Commun. Math. Phys.80, 575–587 (1981)Google Scholar
  6. 6.
    Goddard, P., Nuyts, J., Olive, D.: Gauge theories and magnetic charge. Nucl. Phys. B125, 1 (1977)Google Scholar
  7. 7.
    Hitchin, N.: Monopoles and geodesics. Commun. Math. Phys.83, 579 (1982)Google Scholar
  8. 8.
    Hitchin, N.: On the construction of monopoles. Commun. Math. Phys.89, 145–190 (1983)Google Scholar
  9. 9.
    Humphreys, J.E.: Introduction to Lie algebras and representation theory. Berlin, Heidelberg, New York: Springer 1972 (2nd edn.)Google Scholar
  10. 10.
    Jaffe, A., Taubes, C.: Vortices and monopoles. Boston: Birkhäuser 1980Google Scholar
  11. 11.
    Nahm, W.: The algebraic geometry of multimonopoles. Bonn Preprint, HE-82-30Google Scholar
  12. 12.
    Prasad, M.K.: Yang-Mills-Higgs monopole solutions of arbitrary topological charge. Commun. Math. Phys.80, 137–149 (1981)Google Scholar
  13. 13.
    Taubes, C.H.: The existence of multi-monopole solutions to the non-abelian, Yang-Mills-Higgs equations for arbitrary simple gauge groups. Commun. Math. Phys.80, 343–367 (1981)Google Scholar
  14. 14.
    Ward, R.S.: A Yang-Higgs monopole of charge 2. Commun. Math. Phys.79, 317–325 (1981).Google Scholar
  15. 15.
    Weinberg, E.: Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups. Nucl. Phys. B167, 500 (1980)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • M. K. Murray
    • 1
  1. 1.The Mathematical InstituteOxfordEngland

Personalised recommendations