$R$-matrices for the $n=2,3$ Elliptic Calogero-Moser Models

Braden, H W, Suzuki, T

Published Dec 3, 1993• 6 citations

Abstract

The classical (dynamical) $R$-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent $R$-matrices. The $R$-matrices presented include the dynamical $R$-matrices of Avan and Talon as degenerate cases of the elliptic potential.

Related papers

The non-dynamicalr-matrix structure for the elliptic Calogero-Moser model

Bo-Yu Hou, Wen‐Li Yang

In this paper we construct a new Lax operator for the elliptic Calogero-Moser model with general from the classical dynamical twisting, in which the corresponding r -matrix is purely numerical (non-dynamic). The non-dynamical r -matrix structure of this Lax operator is obtained, which is the elliptic -symmetric r -matrix.

Journal of Physics A Mathematical and GeneralJan 1, 199911 citations

Classical r-matrices for the Elliptic Calogero Model in Harmonic Potential

Shyang-Ling Lou, Yih-Shyan Su

For the classical elliptic Calogero system in an external harmonic potential it is shown that the Lax operator L+L − possesses a classical r-matrix structure. The relation of the r-matrix and the Yang-Baxter equation involving another dynamical matrix are discussed.

Jul 1, 20130 citations

Elliptic Ruijsenaars-Schneider and Calogero-Moser Models Represented by Sklyanin Algebra andsl(n) Gaudin Algebra

Kai Chen, Heng Fan, Bo-Yu Hou +3 more

The relationship between Elliptic Ruijsenaars-Schneider (RS) and Calogero-Moser (CM) models with Sklyanin algebra is presented. Lax pair representations of the Elliptic RS and CM are reviewed. For n=2 case, the eigenvalue and eigenfunction for Lame equation are found by using the result of the Bethe ansatz method.

arXiv:hep-th/0201211Progress of Theoretical Physics SupplementJan 1, 199911 citations

R-matrices for the n = 2,3 elliptic Calogero-Moser models

Harry Whiting Braden, T. Suzuki

arXiv:hep-th/9312031Physics Letters AAug 1, 19948 citations

Classical r -matrix structure for elliptic Ruijsenaars chain and 1 + 1 field analogue of Ruijsenaars–Schneider model

Dmitrii Murinov, Andrei Vladimirovich Zotov

Abstract The classical dynamical r -matrix structure for the periodic elliptic Ruijsenaars chain is described. The Poisson brackets for the monodromy matrix are calculated as well, thus providing Liouville integrability of the model. Next, we study its continuous non-relativistic limit and reproduce the Maillet type non-ultralocal r -matrix structure for the field analogue of the elliptic Calogero–Moser model.

arXiv:2508.12656Journal of Physics A Mathematical and TheoreticalDec 8, 20252 citations

A conjecturedR-matrix

Harry Whiting Braden

A new spectral parameter independent R -matrix (that depends on all of the dynamical variables) is proposed for the elliptic Calogero-Moser models. The necessary and sufficient conditions for the existence this R -matrix reduces to a determinantal equality involving elliptic functions. The required identity appears new and is still unproven in full generality; we present it as conjecture.

arXiv:solv-int/9710011Journal of Physics A Mathematical and GeneralFeb 20, 19988 citations

$R$ -matrices for the $n=2,3$ Elliptic Calogero-Moser Models$R$-matrices for the $n=2,3$ Elliptic Calogero-Moser Models

Braden, H W, Suzuki, T

Published Dec 3, 1993• 6 citations

OpenAlex

Abstract

The classical (dynamical)

R

-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent