Dressing symmetries
Copyright policy )Dressing symmetries
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.
(29 pages)
High Energy Physics - Theory, Applications of global analysis to the sciences, Toda field, FOS: Physical sciences, Heisenberg model, 81T10, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, 81R50, 58F07, Lie-Poisson, High Energy Physics - Theory (hep-th), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], 82B23, dressing transformations, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Quantum groups and related algebraic methods applied to problems in quantum theory
High Energy Physics - Theory, Applications of global analysis to the sciences, Toda field, FOS: Physical sciences, Heisenberg model, 81T10, Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, 81R50, 58F07, Lie-Poisson, High Energy Physics - Theory (hep-th), [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th], 82B23, dressing transformations, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Quantum groups and related algebraic methods applied to problems in quantum theory
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