A Note on the Symplectic Structure on the Dressing Group in the sinh--Gordon Model

Details A Note on the Symplectic Structure on the Dressing Group in the sinh--Gordon Model A Note on the Symplectic Structure on the Dressing Group in the sinh--Gordon Model

1995-10-24

arxiv.org/abs/hep-th/9510174v3

Phys. Lett. B381 (1996) 255

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, latex, no figures, some statements corrected, the end of Sec. 3 and the whole Sec. 4 totally revised

Scientific paper

10.1016/0370-2693(96)00384-X

We analyze the symplectic structure on the dressing group in the \shG\, model by calculating explicitly the Poisson bracket $\{g\x g\}$ where $g$ is the \dg\, element which creates a generic one soliton solution from the vacuum. Our result is that this bracket does not coincide with the Semenov--Tian--Shansky one. The last induces a Lie--Poisson structure on the \dg . To get the bracket obtained by us from the Semenov--Tian--Shansky bracket we apply the formalism of the constrained Hamiltonian systems. The constraints on the \dg\, appear since the element which generates one solitons from the vacuum has a specific form.

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