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Degenerate Integrability of the Spin Calogero–Moser Systems and the Duality with the Spin Ruijsenaars Systems

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Abstract

It is shown that spin Calogero–Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less than half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero–Moser systems in a sense that action-angle variables of one are angle-action variables of the other.

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  1. Department of Mathematics, University of California, Berkeley, CA, 94270, U.S.A.

    N. Reshetikhin

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  1. N. Reshetikhin
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Reshetikhin, N. Degenerate Integrability of the Spin Calogero–Moser Systems and the Duality with the Spin Ruijsenaars Systems. Letters in Mathematical Physics 63, 55–71 (2003). https://doi.org/10.1023/A:1022964224404

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