A lecture on the Calogero-Sutherland models

  • V. Pasquier
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 436)


In these lectures, I review some recent results on the Calogero Sutherland model and the Haldane Shatry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonien and fractional stastistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at a specific coupling constant.


Density Operator Spin Chain Monodromy Matrix Fermi Momentum Dunkl Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F.D.M. Haldane, To appear in “Proceedings of the 16th Taniguchi Symposium”, 1993.Google Scholar
  2. [2]
    C.F.Dunkl, Trans.Amer.Math.Soc, 311 (1989) 167.Google Scholar
  3. [3]
    D.Bernard, M.Gaudin, F.D.M.Haldane and V.Pasquier, J.Phys.A 26 (1993) 5219.Google Scholar
  4. [4]
    F.Lesage, V.Pasquier and D.Serban saclay preprint april 94.Google Scholar
  5. [5]
    B. Sutherland,Phys.Rev A 5 (1972), 1372.Google Scholar
  6. [6]
    C.N.Yang Phys.rev.Letters, 19 (1967) 1312.Google Scholar
  7. [7]
    F.D.M Haldane, Phys.Rev.Lett. 60 (1988) 635.Google Scholar
  8. [8]
    B.S.Shastry, Phys.Rev.Lett. 60 (1988) 639.Google Scholar
  9. [9]
    V.I.Inotzemtsev, J.Stat.Phys.59 (1990) 1143.Google Scholar
  10. [10]
    I.V.Cherednick, preprint march 94.Google Scholar
  11. [11]
    D.Bernard, V.Pasquier and D.Serban saclay preprint april 94.Google Scholar
  12. [12]
    B.D. Simons, P.A. Lee, and B.L. Altshuler, Phys. Rev. Lett. V.70, No26, (1993) 4122.Google Scholar
  13. [13]
    I.G. Macdonald, Séminaire Lotharingien, Publ. I.R.M.A. Strasbourg, 1988Google Scholar
  14. [14]
    R. P. Stanley, Adv. in Math., 77, (1989) 76–115.Google Scholar
  15. [15]
    F.D.M. Haldane, To appear in proceedings of the International Colloquium in Modern Field Theory, Tata institute, 1994.Google Scholar
  16. [16]
    J. Minanan and A.P. Polychronackos CERN preprint april 94.Google Scholar
  17. [17]
    I.V.Cherednick, Invent.Math.106 (1991) 411.Google Scholar
  18. [18]
    A.P.Polychronakos,Phys.Rev.Letters, 69 (1992) 703.Google Scholar
  19. [19]
    V.G.Drinfeld, Funct.Anal.Appl.20 (1988) 56.Google Scholar
  20. [20]
    L.D.Faddeev Les Houches lectures, Elsevier Science Publishers (1984).Google Scholar
  21. [21]
    V.M Buchstaber, G.Felder and A.P. Veselov preprint march 94.Google Scholar
  22. [22]
    M.Gaudin, “la fonction d'onde de Bethe” Masson (1981).Google Scholar
  23. [23]
    I.V.Cherednick, Commun.Math.Phys (1992) 150.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • V. Pasquier
    • 1
  1. 1.Service de Physique Théorique de SaclayGif sur Yvette CedexFrance

Personalised recommendations