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Communications in Mathematical Physics

, Volume 149, Issue 2, pp 279–306 | Cite as

Dressing symmetries

  • Olivier Babelon
  • Denis Bernard
Article

Abstract

We study the group of dressing transformations in soliton theories. We show that it is generated by the monodromy matrix. This provides a new proof of their Lie-Poisson property. We treat in detail the examples of the Toda field theories and the Heisenberg model. We show that the group of dressing transformations is the classical precursor of the various manifestations of quantum groups in these models, e.g. algebraic Bethe ansatz, non-local currents, or quantum group symmetries. Finally, we define field multiplets supporting a linear representation of the dressing group and we show that their exchange algebras are encoded in the classical double.

Keywords

Neural Network Soliton Field Theory Complex System 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 1992

Authors and Affiliations

  • Olivier Babelon
    • 1
  • Denis Bernard
    • 2
  1. 1.Laboratoire de Physique Théorique et Hautes EnergiesUniversité Pierre et Marie CurieParis cedex 05France
  2. 2.Service de Physique Théorique de SaclayGif-sur-YvetteFrance

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