Theoretical and Mathematical Physics

, Volume 103, Issue 3, pp 738–756 | Cite as

Integrals of motion of the classical lattice sine-Gordon system

  • B. Enriquez
  • B. L. Feigin


We compute the local integrals of motions of the classical limit of the lattice sine-Gordon system, using a geometrical interpretation of the local sine-Gordon variables. Using an analogous description of the screened local variables, we show that these integrals are in involution. We present some remarks on relations with the situation at the roots of1 and results on another latticization (linked to the principal subalgebra of
rather than the homogeneous one). Finally, we analyze a module of “screened semilocal variables,” on which the whole


Classical Lattice 
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  1. 1.
    B. L. Feigin,Moscow Lectures (1992).Google Scholar
  2. 2.
    A. G. Izergin and V. E. Korepin, “The lattice quantum sine-Gordon model,”Lett. Math. Phys., No. 5, 199–205 (1981).Google Scholar
  3. 3.
    A. G. Izergin and V. E. Korepin, “Lattice versions of quantum field theory models in two dimensions,”Nucl. Phys.,B205, 401–413 (1982).Google Scholar
  4. 4.
    M. A. Semenov-Tian-Shansky, “Dressing action transformations and Poisson-Lie group actions,”Publ. Math. RIMS,21, 1237–1260 (1985).Google Scholar
  5. 5.
    A. Guichardet,Cohomologie des groupes topologiques et des algèbres de Lie, Cedic/Fernand Nathan.Google Scholar
  6. 6.
    B. L. Feigin and E. Frenkel,Generalized KdV flows and nilpotent subgroups of affine Kac-Moody groups, Preprint hep-th 9311171.Google Scholar
  7. 7.
    L. D. Faddeev and A. Yu. Volkov,Abelian current algebra and the Virasoro algebra on the lattice, Preprint HV-TFT 93-29;Phys. Lett. B (to appear).Google Scholar
  8. 8.
    V. G. Drinfeld and V. V. Sokolov, “Lie algebras and equations of Korteweg-deVries type,”J. Sov. Math.,30, 1975–2036 (1985).Google Scholar
  9. 9.
    B. Enriquez, “Nilpotent action on the KdV variables and 2-dimensional DS reduction,”Teor. Mat. Fiz. (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • B. Enriquez
    • 1
    • 2
  • B. L. Feigin
    • 1
    • 2
  1. 1.Centre de MathématiquesPalaiseau CedexFrance
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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