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Communications in Mathematical Physics

, Volume 144, Issue 2, pp 215–234 | Cite as

On multivortices in the electroweak theory II: Existence of Bogomol'nyi solutions in ℝ2

  • Joel Spruck
  • Yisong Yang
Article

Abstract

In this paper we study the Bogomol'nyi equations of the electroweak theory in the full plane. We will show that, for any distribution of the vortices, there exists a two parameter family of gauge-distinct solutions. Moreover, we also establish some sharp decay rate estimates for these solutions.

Keywords

Vortex Neural Network Statistical Physic Complex System Decay Rate 
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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References

  1. 1.
    Ambjorn, J., Nielsen, N. K., Olesen, P.: Superconducting cosmic strings andW condensation. Nucl. Phys.B310, 625–635 (1988)Google Scholar
  2. 2.
    Ambjorn, J., Olesen, P.: Anti-screening of large magnetic fields by vector bosons. Phys. Lett.B214, 565–569 (1988)Google Scholar
  3. 3.
    Ambjorn, J., Olesen, P.: A magnetic condensate solution of the classical electroweak theory. Phys. Lett.B218, 67–71 (1989)Google Scholar
  4. 4.
    Ambjorn, J., Olesen, P.: On electroweak magnetism. Nucl. Phys.B315, 606–614 (1989)Google Scholar
  5. 5.
    Jaffe, A., Taubes, C. H.: Vortices and Monopoles. Boston: Birkhäuser 1980Google Scholar
  6. 6.
    McOwen, R.: Conformal metric in ℝ2 with prescribed Gaussian curvature and positive total curvature. Indiana Univ. Math. J.34, 97–104 (1985)Google Scholar
  7. 7.
    Spruck, J., Yang, Y.: On multivortices in the electroweak theory I: Existence of periodic solutions. Commun. Math. Phys.144, 1–16 (1992)Google Scholar
  8. 8.
    't Hooft, G.: A property of electric and magnetic flux in nonabelian gauge theories. Nucl. Phys.B153, 141–160 (1979)Google Scholar
  9. 9.
    Yang, Y.: Existence of the massiveSO(3) vortices. J. Math. Phys.32, 1395–1399 (1991)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Joel Spruck
    • 1
  • Yisong Yang
    • 2
  1. 1.Department of MathematicsUniversity of MassachusettsAmherstUSA
  2. 2.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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