Dynamical $r$-matrices for the Elliptic Calogero-Moser Model

Details Dynamical $r$-matrices for the Elliptic Calogero-Moser Model Dynamical $r$-matrices for the Elliptic Calogero-Moser Model

1993-08-12

arxiv.org/abs/hep-th/9308060v1

Alg.Anal. 6 (1994) 227-237; St.Petersburg Math.J. 6 (1995) 397-406

Physics

High Energy Physics

High Energy Physics - Theory

11p, LATEX file, LPTHE-93-42

Scientific paper

For the integrable $N$-particle Calogero-Moser system with elliptic potential it is shown that the Lax operator found by Krichever possesses a classical $r$-matrix structure. The $r$-matrix is a natural generalisation of the matrix found recently by Avan and Talon (hep-th/9210128) for the trigonometric potential. The $r$-matrix depends on the spectral parameter and only half of the dynamical variables (particles' coordinates). It satisfies a generalized Yang-Baxter equation involving another dynamical matrix.

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