Dressing symmetries

Olivier Babelon , Denis Bernard (1)

1 SPhT - Service de Physique Théorique

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.

Domaines: Physique mathématique [math-ph]; Physique des Hautes Energies - Théorie [hep-th]

Olivier Babelon, Denis Bernard. Dressing symmetries. Communications in Mathematical Physics, 1992, 149 (2), pp.279-306. ⟨10.1007/BF02097626⟩. ⟨hal-03370765⟩