Tamás F. Görbe, “A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero–Moser System”, SIGMA, 2016, Volume 12,027, 5 pp.

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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

Abstract: 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.

Keywords: integrable systems; Calogero–Moser type systems; spectral coordinates; Hamiltonian reduction; action-angle duality.

MSC: 14H70; 37J15; 53D20

Received: January 19, 2016; in final form March 8, 2016; Published online March 11, 2016

Language: English

DOI: 10.3842/SIGMA.2016.027