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On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)

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arxiv hep-th/9906240 v1 pith:STC7JKJD submitted 1999-06-29 hep-th

classification hep-th
keywords coordinatemomentumdualityellipticfamilyhamiltoniansargumentcase
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We construct a two parameter family of 2-particle Hamiltonians closed under the duality operation of interchanging the (relative) momentum and coordinate. Both coordinate and momentum dependence are elliptic, and the modulus of the momentum torus is a non-trivial function of the coordinate. This model contains as limiting cases the standard Ruijsenaars-Calogero and Toda family of Hamiltonians, which are at most elliptic in the coordinates, but not in the momenta.

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Cited by 1 Pith paper

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  1. Classical elliptic integrable systems from the moduli space of instantons

    math-ph 2024-12 conditional novelty 4.0 of 10

    A review that derives Krichever's elliptic Calogero-Moser Lax matrix from qq-characters of instanton moduli spaces, with K-theoretic and elliptic counterparts, plus Lax eigenvectors from folded instantons.

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