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

R. Sasaki; K. Takasaki

doi:10.1063/1.2162334

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arXiv · hep-th/0510035

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

R. Sasaki·K. Takasaki

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Abstract

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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R. Sasaki, K. Takasaki. 2005-10-05. Explicit solutions of the classical Calogero & Sutherland systems for any root system. https://doi.org/10.1063/1.2162334

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