Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model

Details Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model

2001-01-18

arxiv.org/abs/nlin/0101033v2

Phys.Atom.Nucl. 65 (2002) 1042-1046; Yad.Fiz. 65 (2002) 1075-1079

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, ReVTeX, no figures. Based on talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, J

Scientific paper

10.1134/1.1490107

Relations between the free motion on the GL^+(n, R) group manifold and the dynamics of an n-particle system with spin degrees of freedom on a line interacting with the pairwise 1/sinh^2 x ``potential'' (Euler-Calogero-Sutherland model) is discussed in the framework of Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: due to the continuous invariance and due to the discrete symmetry. It is shown that after projection on the corresponding invariant manifolds the resulting Hamiltonian system represents the Euler-Calogero-Sutherland model in both cases.

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