Conservation laws in the continuum $1/r^2$ systems

Details Conservation laws in the continuum $1/r^2$ systems Conservation laws in the continuum $1/r^2$ systems

1995-11-23

arxiv.org/abs/cond-mat/9511115v1

Physics

Condensed Matter

19 RevTeX 3.0 pages with 2 PS-figures included

Scientific paper

10.1088/0305-4470/29/15/033

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 to resum 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 explicit construction.

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