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Structures in BC_N Ruijsenaars-Schneider models | | J. Avan
; G. Rollet
; | | Date: |
13 Jun 2001 | | Journal: | J.Math.Phys. 43 (2002) 403-416 | | Subject: | Exactly Solvable and Integrable Systems; Quantum Algebra | nlin.SI hep-th math.QA | | Abstract: | We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket behavior, although the dynamical dependence is more complicated. Commuting Hamiltonians stemming from the BC_N Ruijsenaars-Schneider Lax matrix are shown to be linear combinations of particular Koornwinder-van Diejen ``external fields’’ Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings. Uniqueness of such commuting Hamiltonians is established once the first of them and the general analytic structure are given. | | Source: | arXiv, nlin.SI/0106015 | | Services: | Forum | Review | PDF | Favorites | |
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