SIGMA 12 (2016), 027, 5 pages arXiv:1601.01181
A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero-Moser System
Tamás F. Görbe
Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged, Hungary
Received January 19, 2016, in final form March 08, 2016; Published online March 11, 2016
We use Hamiltonian reduction to simplify Falqui and Mencattini's recent proof of Sklyanin's expression providing spectral Darboux coordinates of the rational Calogero-Moser system. This viewpoint enables us to verify a conjecture of Falqui and Mencattini, and to obtain Sklyanin's formula as a corollary.
integrable systems; Calogero-Moser type systems; spectral coordinates; Hamiltonian reduction; action-angle duality.
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