Classical R-matrix structure for the Calogero model
نویسندگان
چکیده
منابع مشابه
The r-matrix structure of the Euler-Calogero-Moser model
We construct the r-matrix for the generalization of the Calogero-Moser system introduced by Gibbons and Hermsen. By reduction procedures we obtain the r-matrix for the O(N) Euler-Calogero-Moser model and for the standard AN Calogero-Moser model. PAR LPTHE 93-55 L.P.T.H.E. Université Paris VI (CNRS UA 280), Box 126, Tour 16, 1 étage, 4 place Jussieu, F-75252 PARIS CEDEX 05
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In this paper, we construct a new Lax operator for the elliptic An−1 Calogero-Moser model with general n(2 ≤ n) from the classical dynamical twisting, in which the corresponding r-matrix is purely numeric (nondynamical one). The nondynamical r-matrix structure of this Lax operator is obtained, which is elliptic Zn-symmetric r-matrix. Mathematics Subject Classification : 70F10 , 70H33 , 81U10.
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The elliptic Calogero-Moser (CM) model[1-4] is the system of N one-dimensional particles interacting by two-particle potential of the elliptic type. It is well-known that the CM model is completely integrable[18]. The Lax operator of this system , which is the most effective way to construct the complete set of integrals of motion, was found by Krichever[6] . The classical r-matrix structure of...
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متن کاملar X iv : h ep - t h / 92 10 12 8 v 1 2 3 O ct 1 99 2 Classical R - matrix structure for the Calogero model
A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero-Olshanetski-Perelomov. This R-matrix is dynamical, non antisymmetric and non-invertible. It immediately triggers the integrability of the Type I, II and III potentials, and the algebraic structures associated with the Type V potential.
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ژورنال
عنوان ژورنال: Physics Letters B
سال: 1993
ISSN: 0370-2693
DOI: 10.1016/0370-2693(93)90039-k