Solitons as sections in non trivial bundles

  • Luis J. Boya
  • Juan Mateos
Gauge Theories
Part of the Lecture Notes in Physics book series (LNP, volume 135)


We interpret soliton solutions to classical wave equations as sections in some vector bundles; the peculiarity of soliton behaviour comes from the non-trivial character of the fibration, which also includes the “broken symmetry” aspect. We review in this light the most well-known cases: Kink, sine-Gordon soliton, vortex, monopole and instanton, and make contact with the former homotopy classification through the construction of bundles over spheres.


Vector Bundle Line Bundle Fibre Bundle Chern Class Trivial Bundle 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Luis J. Boya
    • 1
  • Juan Mateos
  1. 1.Departamento de Física Teórica Facultad de Ciencias Universidad de SalamancaSalamancaSpain

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