6 v 2 2 1 Ju n 20 01 The Lax pair for C 2 - type Ruijsenaars - Schneider model ∗
نویسنده
چکیده
We study the C2 Ruijsenaars-Schneider(RS) model with interaction potential of trigonometric type. The Lax pairs for the model with and without spectral parameter are constructed. Also given are the involutive Hamiltonians for the system. Taking nonrelativistic limit, we obtain the Lax pair of C2 Calogero-Moser model.
منابع مشابه
0 The Lax pair for C 2 - type Ruijsenaars - Schneider model
We study the C2 Ruijsenaars-Schneider(RS) models with interaction potentials of rational and trigonometric types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking nonrelativistic limit, we obtain the Lax pair of C2 Calogero-Moser model. PACS: 02.20.+b, 11.10.Lm, 03.80.+r
متن کاملThe D n Ruijsenaars - Schneider model
The Lax pair of the Ruijsenaars-Schneider model with interaction potential of trigonometric type based on Dn Lie algebra is presented. We give a general form for the Lax pair and prove partial results for small n. Liouville integrability of the corresponding system follows a series of involutive Hamiltonians generated by the characteristic polynomial of the Lax matrix. The rational case appears...
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 کاملar X iv : h ep - t h / 96 02 16 0 v 2 2 0 M ay 1 99 6 Why are the
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 کاملStructures in Bc N Ruijsenaars-schneider Models
We construct the classical r-matrix structure for the Lax formulation of BC N Ruijsenaars-Schneider systems proposed in [18]. The r-matrix structure takes a quadratic form similar to the A N Ruijsenaars-Schneider Poisson bracket behavior, although the dy-namical dependence is more complicated. Commuting Hamiltonians stemming from the BC N Ruijsenaars-Schneider Lax matrix are shown to be linear ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008