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Communications in Mathematical Physics

, Volume 158, Issue 2, pp 241–266 | Cite as

Monopoles, braid groups, and the dirac operator

  • Ralph L. Cohen
  • John D. S. Jones
Article

Abstract

Using the relation between the space of rational functions on ℂ, the space ofSU(2)-monopoles on ℝ3, and the classifying space of the braid group, see [10], we show how the index bundle of the family of real Dirac operators coupled toSU(2)-monopoles can be described using permutation representations of Artin's braid groups. We also show how this implies the existence of a pair consisting of a gauge fieldA and a Higgs field Φ on ℝ3 whose corresponding Dirac equation has an arbitrarily large dimensional space of solutions.

Keywords

Neural Network Statistical Physic Complex System Rational Function Nonlinear Dynamics 
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.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Ralph L. Cohen
    • 1
  • John D. S. Jones
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Mathematics InstituteUniversity of WarwickCoventryEngland

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