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- W2061287917 abstract "The canonical transformation approach generated by the semisimple subgroup GCM(3)⊂Sp(6,R) is applied to reduction of the Lie–Poisson bracket on coadjoint orbits of the Sp(6,R) group and the Poisson coalgebra spO*(6) is determined. Investigating the construction of the N-particle phase, induced by this reduction, we identify the Poisson coalgebra spO*(6) as the algebra of quadratic O(K), K≡N−1 invariant forms on symplectic 6 K−12 dimensional phase space T*[O(K−3)O(K)], K⩾3. The general classification scheme of Poisson orbits for spO*(6) is found and applied to the classification of coadjoint orbits of the Sp(6,R) group occurring in the decomposition of N-particle phase spaces. We show that the spO*(k), k=4,6 Poisson action on some class of surfaces determined by Casimir invariants is not transitive. The Poisson maps for all classes of orbits spO*(4) and spO*(6) are found. The quantum unitary irreducible representations of spO*(4) are obtained." @default.
- W2061287917 created "2016-06-24" @default.
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- W2061287917 date "2003-05-21" @default.
- W2061287917 modified "2023-09-26" @default.
- W2061287917 title "Application of Poisson maps on coadjoint orbits of Sp(6,R) group to many body dynamics" @default.
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- W2061287917 doi "https://doi.org/10.1063/1.1571222" @default.
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