ar X iv : h ep - t h / 95 05 01 1 v 1 2 M ay 1 99 5 Knizhnik - Zamolodchikov equations and the Calogero - Sutherland - Moser integrable models with exchange terms

ar 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...

ar X iv : h ep - t h / 95 05 07 1 v 1 1 2 M ay 1 99 5 EXCHANGE OPERATORS AND EXTENDED HEISENBERG ALGEBRA FOR THE THREE - BODY CALOGERO - MARCHIORO - WOLFES PROBLEM

The exchange operator formalism previously introduced for the Calogero problem is extended to the three-body Calogero-Marchioro-Wolfes one. In the absence of oscillator potential, the Hamiltonian of the latter is interpreted as a free particle Hamiltonian, expressed in terms of generalized momenta. In the presence of oscillator potential, it is regarded as a free modified boson Hamiltonian. The...

ar X iv : h ep - t h / 95 05 05 9 v 1 1 0 M ay 1 99 5 orthochronous The Conformal Spin and Statistics Theorem

ar X iv : h ep - t h / 93 05 01 5 v 1 5 M ay 1 99 3 PAR – LPTHE 92 – 16 February 1 , 2008 TOWARDS THREE - DIMENSIONAL BETHE ANSATZ

We introduce a " pre-Bethe-Ansatz " system of equations for three dimensional vertex models. We bring to the light various algebraic curves of high genus and discuss some situations where these curves simplify. As a result we describe remarkable subvarieties of the space of parameters.

ar X iv : h ep - t h / 94 12 17 0 v 1 1 9 D ec 1 99 4 Integrable Time - Discretisation of the Ruijsenaars - Schneider Model

An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was introduced for the first time by Ruijsenaars and Schneider. For the discrete-time model the equations of motion take the form of Bethe Ansatz equations for the inhomogeneous spin– 1 2 Heisenberg magnet. W...