arXiv : hep - th / 9603039 v 1 7 Mar 1996 1
نویسنده
چکیده
We extend our previous analysis of the classical integrable models of Calogero in several respects. Firstly we provide the algebraic resaons of their quantum integrability.Secondly we show why these systems allow their initial value problem to be solved in closed form. Furthermore we show that due to their similarity with the above models the classical and quantum Heisenberg magnets with long rang interactions in a magnetic field are also intergrable. Explicit expressions are given for the integrals of motion in involution in the classical case and for the commuting operators in the quantum case.
منابع مشابه
arXiv : hep - th / 9602161 v 1 28 Feb 1996 1
We show that the integrability of the dynamical system recently proposed by Calogero and characterized by the Hamiltonian H = ∑N j,k pjpk{λ+μcos[ν(qj−qk)]} is due to a simple algebraic structure . It is shown that the integrals of motion are related to the Casimiar invariants of of the su(1, 1) algebra. Our method shows clearly how these types of systems can be generalized .
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