Communications in Mathematical Physics

, Volume 59, Issue 2, pp 109–116 | Cite as

Properties of certain matrices related to the equilibrium configuration of the one-dimensional many-body problems with the pair potentialsV1(x)=−log ∣sinx∣ andV2(x)=1/sin2x

  • F. Calogero
  • A. M. Perelomov


It is shown that at equilibrium certain matrices associated to the one-dimensional many-body problems with the pair potentialsV1(x)=−log∣sinx∣ andV2(x)=1/sin2x have a very simple structure. These matrices are those that characterize the small oscillations of these systems around their equilibrium configurations, and, for the second system, the Lax matrices that demonstrate its integrability.


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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • F. Calogero
    • 1
    • 2
  • A. M. Perelomov
    • 3
  1. 1.Istituto di FisicaUniversità di RomaRomaItaly
  2. 2.Istituto Nazionale di Fisica NucleareSezione di RomaRomaItaly
  3. 3.Institute of Theoretical and Experimental PhysicsMoscowUSSR

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