On double-elliptic integrable systems: 1. A duality argument for the case of SU(2) Original Research Article

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.