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Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model | | A.M. Khvedelidze
; D.M. Mladenov
; | | Date: |
18 Dec 2000 | | Journal: | Phys.Atom.Nucl. 65 (2002) 1042-1046; Yad.Fiz. 65 (2002) 1075-1079 | | Subject: | Exactly Solvable and Integrable Systems; Mathematical Physics | nlin.SI hep-th math-ph math.MP | | Abstract: | 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. | | Source: | arXiv, nlin.SI/0101033 | | Services: | Forum | Review | PDF | Favorites | |
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