Topological Particles

  • Michael Monastyrsky
Part of the Modern Birkhäuser Classics book series (MBC)


In 1974 the Dutch physicist Gerardt’t Hooft and the Russian physicist Alexander M. Polyakov (now at Princeton University) found solutions to the Yang-Mills equation for the group SO(3) and additional scalar fields (the fields of Goldstone- Higgs).1 These solutions had one topological charge which was interpreted as a “magnetic charge.” G.’t Hooft suggested calling them magnetic monopoles. The name was to symbolize the deep commonality of the newly discovered “particle” with another mysterious object—the Dirac magnetic monopole.


Magnetic Charge Topological Charge Homotopy Group Vacuum Solution Magnetic Monopole 
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  1. 1.
    Before the discovery of neutral currents, the Georgi-Glashow model of weak interactions competed with the Weinberg-Salam model.Google Scholar
  2. 2.
    RA.M. Dirac, Proc. Roy. Soc, A. 133 (1931), p. 60.CrossRefGoogle Scholar
  3. 3.
    Spaces homeomorphic, but not diffeomorphic, to ℝ4 are called “fake” ℝ4,s and denoted ℝ4 f. They have amazing topological properties. For example, in contrast to the standard R4, the spaces ℝ4 f contain a compact set K that cannot be enclosed in any smoothly imbedded sphere S3, although this can be done with a continuously imbedded sphere. It follows from this that the spheres in ℝ4 have a complicated (sawtooth) fractal structure near infinity.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Michael Monastyrsky
    • 1
  1. 1.Department of Theoretical PhysicsInsitute for Theoretical and Experimental PhysicsMoscowRussia

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