A pr 1 99 6 Elliptic Ruijsenaars – Schneider and Calogero – Moser hierarchies are governed by the same r – matrix
نویسنده
چکیده
We demonstrate that in a certain gauge the elliptic Ruijsenaars– Schneider models admit Lax representation governed by the same dynamical r– matrix as their non–relativistic counterparts (Calogero–Moser models). This phenomenon was previously observed for the rational and hyperbolic models.
منابع مشابه
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We demonstrate that in a certain gauge the Lax matrices of the rational and hyperbolic Ruijsenaars–Schneider models have a quadratic r-matrix Poisson bracket which is an exact quadratization of the linear r–matrix Poisson bracket of the Calogero–Moser models. This phenomenon is explained by a geometric derivation of Lax equations for arbitrary flows of both hierarchies, which turn out to be gov...
متن کاملThe dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider model
From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruijsenaars’). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero-Moser model. Mathematics Subject Classification : 70F10 , 70H33...
متن کاملThe dynamical twisting and nondynamical r-matrix structure for the elliptic Ruijsenaars-Schneider model
From the dynamical twisting of the classical r-matrix, we obtain a new Lax operator for the elliptic Ruijsenaars-Schneider model (cf. Ruisenaars’). The corresponding r-matrix is shown to be the classical Zn-symmetric elliptic r-matrix, which is the same as that obtained in the study of the nonrelativistic version—the An−1 Calogero-Moser model givened by us. Mathematics Subject Classification : ...
متن کاملThe Nondynamical R-matrix Structure of the Elliptic Ruijsenaars-schneider Model with N=2
We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model ) in the same gauge.The relation between our (classical) Lax operator and the Lax operator given by Ruijsenaars is also obtained. Mathematics Subject...
متن کاملThe Classical R-matrix for the Relativistic Ruijsenaars-schneider System
We compute the classical r-matrix for the relativistic generalization of the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the speed-of-light parameter λ. We connect it with the non-relativistic Calogero-Moser r-matrix (λ → −1) and the λ = 1 sine-Gordon soliton limit.
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