CONSERVATION-LAWS IN THE CONTINUUM 1 R(2) SYSTEMS/

We study the conservation laws of both the classical and me quantum me chanical continuum 1/r(2) type systems. For the classical case, we int roduce new integrals of motion along the recent ideas of Shastry and S utherland (SS), supplementing the usual integrals of motion constructe d much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The differenc e of these two sets of integrals then gives rise to yet another comple te set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We g ive 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 in tegrals of SS by explicit construction. Finally, we go to the asymptot ic or low-density limit and derive recursion relations of the two sets of asymptotic integrals.