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Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models. (English. Russian original) Zbl 0692.35105

J. Sov. Math. 47, No. 2, 2413-2423 (1989); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 164, 67-79 (1987).
Summary: Explicit solutions are presented to the recursion relation arising in the calculation of correlator functions in exactly solvable models of QFT via a method proposed by V. Korepin. The solutions are expressed as determinants of certain matrices.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81T99 Quantum field theory; related classical field theories
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References:

[1] A. G. Izergin and V. E. Korepin, ”The quantum inverse scattering method approach to correlation functions,” Commun. Math. Phys.,94, 67–92 (1984). · Zbl 1093.82504 · doi:10.1007/BF01212350
[2] A. G. Izergin and V. E. Korepin, ”Correlation functions for the Heisenberg XXZ-antiferromagnet,” Commun. Math. Phys.,99, 271–302 (1985). · Zbl 1094.82503 · doi:10.1007/BF01212283
[3] D. B. Creamer, H. B. Thacker, and D. Wilkinson, ”Gelfand-Levitan method for operator fields,” Phys. Rev.,D21, 1523–1528 (1980).
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[8] A. G. Izergin, ”Statistical sum of six-vertex model in finite volume,” Dokl. Akad. Nauk SSSR,295, No. 6, 1603–1609 (1987).
[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).
[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).
[11] I. MacDonald, Symmetric Functions and Hall Polynomials [Russian translation], Mir, Moscow (1985). · Zbl 0672.20007
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