Journal of Soviet Mathematics

, Volume 47, Issue 2, pp 2413–2423 | Cite as

Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models

  • A. N. Kirillov
  • F. A. Smirnov
Article
  • 31 Downloads

Abstract

In this paper the recursion relations which arise in calculating correlators in exactly solvable models by the method of V. E. Korepin are explicitly solved. The solution is given in the form of determinants of certain matrices.

Keywords

Solvable Model Recursion Relation Combinatorial Problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    A. G. Izergin and V. E. Korepin, “The quantum inverse scattering method approach to correlation functions,” Commun. Math. Phys.,94, 67–92 (1984).CrossRefGoogle Scholar
  2. 2.
    A. G. Izergin and V. E. Korepin, “Correlation functions for the Heisenberg XXZ-antiferromagnet,” Commun. Math. Phys.,99, 271–302 (1985).Google Scholar
  3. 3.
    D. B. Creamer, H. B. Thacker, and D. Wilkinson, “Gelfand-Levitan method for operator fields,” Phys. Rev.,D21, 1523–1528 (1980).Google Scholar
  4. 4.
    F. A. Smirnov, “Gel'fand-Levitan equations for quantum nonlinear Schrödinger equation with attraction,” Dokl. Akad. Nauk SSSR,262, 78–83 (1982).Google Scholar
  5. 5.
    D. B. Creamer, H. B. Thacker, and D. Wilkinson, “A study of correlation functions for delta-function Bose gas,” Fermilab-Pub.-85/51-T, April, 1985.Google Scholar
  6. 6.
    A. N. Kirillov and F. A. Smirnov, “Formactors in SU(2)-invariant Thirring model,” J. Sov. Math.,47, No. 2 (1989).Google Scholar
  7. 7.
    F. A. Smirnov, “A general formula for soliton formfactors in the quantum sine-Gordon model,” J. Phys. A: Math. Gen.,19, L575-L578 (1986).CrossRefGoogle Scholar
  8. 8.
    A. G. Izergin, “Statistical sum of six-vertex model in finite volume,” Dokl. Akad. Nauk SSSR,295, No. 6, 1603–1609 (1987).Google Scholar
  9. 9.
    A. N. Kirillov and F. A. Smirnov, “Form factors in O(3) nonlinear a-model,” Int. J. Mod. Phys., A,2, No. 6 (1987).Google Scholar
  10. 10.
    A. G. Izergin, V. E. Korepin, and N. Yu. Reshetikhin, “Correlation functions of fields in a one-dimensional Bose gas,” J. Sov. Math.,46, No. 1 (1989).Google Scholar
  11. 11.
    I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Mir, Moscow (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • A. N. Kirillov
  • F. A. Smirnov

There are no affiliations available

Personalised recommendations