Rudolf, Romer A and Shastry, Siriam B and Sutherland, Bill (1996) Conservation laws in the continuum $1/r^2$systems. In: Journal of Physics A (Mathematical and General), 29 (15). pp. 4699-4714.
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We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland(SS),supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need toresum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicitconstruction.Finally, we go to the asymptotic or low-density limit and derive recursion relations of the two sets of asymptotic integrals.
|Item Type:||Journal Article|
|Additional Information:||Copyright of this article belongs to Institute of Physics|
|Department/Centre:||Division of Physical & Mathematical Sciences > Physics|
|Date Deposited:||23 Sep 2006|
|Last Modified:||19 Sep 2010 04:31|
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