Explicit solutions of the classical Calogero & Sutherland systems for any root system

Details Explicit solutions of the classical Calogero & Sutherland systems for any root system Explicit solutions of the classical Calogero & Sutherland systems for any root system

2005-10-05

arxiv.org/abs/hep-th/0510035v1

J.Math.Phys. 47 (2006) 012701

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LaTeX, no figure

Scientific paper

10.1063/1.2162334

Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works for Calogero & Sutherland systems based on any root system. It generalises the well-known results by Olshanetsky and Perelomov for the A type root systems. Explicit solutions of the (rational and trigonometric) higher Hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems.

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