Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems

Details Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems

2003-05-14

arxiv.org/abs/hep-th/0305120v1

J.Phys.A37:469-480,2004

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e with amsfonts 15 pages, no figures

Scientific paper

10.1088/0305-4470/37/2/015

The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider systems, which are one parameter deformation of Calogero-Moser systems, is addressed. Many remarkable properties of classical Calogero and Sutherland systems (based on any root system) at equilibrium are reported in a previous paper (Corrigan-Sasaki). For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all "integer valued". In this paper we report that similar features and results hold for the Ruijsenaars-Schneider type of integrable systems based on the classical root systems.

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