Theoretical and Mathematical Physics

, Volume 92, Issue 2, pp 837–842 | Cite as

Quantum inverse scattering method on a spacetime lattice

  • A. Yu. Volkov
  • L. D. Faddeev


The formalism of the quantum inverse scattering method is developed on a lattice in spacetime that imitates light cone coordinates. The zero-curvature representation makes it possible to introduce in a natural manner operators of displacement along the coordinate axes. The method is illustrated for the example of the sine—Gordon system.


Sine Manner Operator Light Cone Inverse Scattering Natural Manner 
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  1. 1.
    E. K. Sklyanin, L. A. Takhmadzhyan, and L. D. Faddeev,Teor. Mat. Fiz.,40, 194 (1979).Google Scholar
  2. 2.
    L. A. Takhmadzhyan and L. D. Faddeev,Usp. Mat. Nauk,34, 13 (1979).Google Scholar
  3. 3.
    L. A. Takhmadzyan and L. D. Faddeev,The Hamiltonian Approach in the Theory of Solitons [in Russian], Nauka, Moscow (1986).Google Scholar
  4. 4.
    V. O. Tarasov, L. A. Takhmadzhyan, and L. D. Faddeev,Teor. Mat. Fiz.,57, 163 (1983).Google Scholar
  5. 5.
    R. Hirota,J. Phys. Soc. Jpn.,43, 2079 (1977).Google Scholar
  6. 6.
    V. G. Papageorgiou, F. W. Nijhoff, and H. W. Capel,Phys. Lett. A,147, 106 (1990).Google Scholar
  7. 7.
    F. W. Nijhoff, V. G. Papageorgiou, and H. W. Capel, in:Quantum Groups (ed. P. Kulish), Springer (1992).Google Scholar
  8. 8.
    L. D. Faddeev and N. Yu. Reshetikhin,Ann. Phys. (N.Y.),167, 227 (1986).Google Scholar
  9. 9.
    C. Destri and H. J. De Vega,Nucl. Phys. B,290, 363 (1987).Google Scholar
  10. 10.
    L. D. Faddeev, in:Fields and Particles (eds. H. Mitter and W. Schweiger), Springer (1990).Google Scholar
  11. 11.
    V. E. Zakharov and A. V. Mikhailov,Zh. Eksp. Teor. Fiz.,69, 1654 (1975).Google Scholar
  12. 12.
    E. K. Sklyanin,Zap. Nauchn. Semin. LOMI,95, 53 (1980).Google Scholar
  13. 13.
    A. G. Izergin and V. E. Korepin,Lett. Math. Phys.,5, 199 (1981).Google Scholar
  14. 14.
    J.-L. Gervais,Phys. Lett. B,160, 279 (1985).Google Scholar
  15. 15.
    A. Yu. Volkov,Teor. Mat. Fiz.,74, 135 (1988).Google Scholar
  16. 16.
    A. Yu. Volkov, Preprint TPT, Helsinki (1992).Google Scholar
  17. 17.
    V. V. Bazhanov and Yu. G. Stroganov,J. Stat. Phys.,51, 799 (1990).Google Scholar
  18. 18.
    A. Yu. Volkov, Candidate's Dissertation [in Russian], Leningrad Branch, V. A. Steklov Mathematics Institute, Leningrad (1987).Google Scholar
  19. 19.
    V. Fateev and A. V. Zamolodchikov,Phys. Lett. A,92, 37 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • A. Yu. Volkov
  • L. D. Faddeev

There are no affiliations available

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