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arXiv · hep-th/9111036

Dressing Symmetries

O. Babelon·D. Bernard
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Abstract

We study Lie-Poisson actions on symplectic manifolds. We show that they are generated by non-Abelian Hamiltonians. We apply this result to the group of dressing transformations in soliton theories; we find that the non-Abelian Hamiltonian is just the monodromy matrix. This provides a new proof of their Lie-Poisson property. We show that the dressing transformations are the classical precursors of the non-local and quantum group symmetries of these theories. We treat in detail the examples of the Toda field theories and the Heisenberg model.

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O. Babelon, D. Bernard. 1991-11-20. Dressing Symmetries. https://doi.org/10.1007/bf02097626

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