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Yang-Baxter equation and reflection equations in integrable models

  • P. P. Kulish
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 469)

Keywords

Integrable Model Quantum Group Braid Group Conformal Field Theory Monodromy Matrix 
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.

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References

  1. 1.
    L. D. Faddeev, Integrable models in (1+1)-dimensional quantum, field theory, Proceed. Les Houches XXXIX, (eds J.-B. Zuber and R. Stora), North-Holland Publ., 1984, 561–608.Google Scholar
  2. 2.
    L. D. Faddeev and L. A. Takhtajan, Russ. Math. Surveys 34 (1979) 11–68.ADSGoogle Scholar
  3. 3.
    P. P. Kulish and E. K. Sklyanin, Lect. Notes Phys. 151 (1982) 61–119.ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    H. B. Thacker, Rev. Mod. Phys. 53 (1981) 253–285.CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    A. G. Izergin and V. E. Korepin, Sov. J. Part. Nucl. 13 (1982) 207–223.MathSciNetGoogle Scholar
  6. 6.
    H. J. de Vega, Int. J. Mod. Phys. A4 (1989) 2371–2463.CrossRefADSzbMATHGoogle Scholar
  7. 7.
    E. K. Sklyanin, Quantum inverse scattering method: selected topics, in: Quantum group and quantum integrable systems, (ed. M.-L. Ge), Singapore: WS, 1992.Google Scholar
  8. 8.
    F. W. Nijhoff and H. W. Capel, Quantization of integrable mappings, in: Geometric and quantum aspects of integrable systems, (ed. G. F. Helsmincle), Lect. Notes Phys. 424 (1993) 187–211.Google Scholar
  9. 9.
    M. Jimbo (ed.) Yang-Baxter equation in integrable systems, Singapore: WS, 1990, 715 pp.zbMATHGoogle Scholar
  10. 10.
    E. H. Lieb and D. C. Mattis (eds.), Mathematical Physics in one dimension, NY-London: Acad. Press, 1966.Google Scholar
  11. 11.
    R. J. Baxter, Exactly solved models in statistical mechanics, NY-London: Acad. Press, 1982.zbMATHGoogle Scholar
  12. 12.
    M. Gaudin, La fonction d'onde de Bethe, Paris: Masson, 1983.zbMATHGoogle Scholar
  13. 13.
    L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Berlin: Springer-Verlag, 1987.zbMATHGoogle Scholar
  14. 14.
    F. A. Smirnov, Form factors in completely integrable models of quantum field theory, Singapore: WS, 1992.zbMATHGoogle Scholar
  15. 15.
    V. E. Korepin, N. M. Bogoliubov and A. G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge University Press, 1993.Google Scholar
  16. 16.
    M. Jimbo and T. Miwa, Algebraic analysis of solvable lattice models, CBMS/85N, 1994.Google Scholar
  17. 17.
    C. Gómez, M. Ruiz-Altaba and G. Sierra, Quantum groups in two-dimensional physics, Cambridge University Press, 1995 (to be published).Google Scholar
  18. 18.
    E. Abdalla, M. C. B. Abdalla and K. Rothe, Non perturbative methods in two dimensional quantum field theory, WS, Singapore, 1991.Google Scholar
  19. 19.
    A. Zamolodchikov and Al. Zamolodchikov, Ann. Phys. 120 (1979) 253.CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    C. N. Yang, Phys. Rev. Lett. 19 (1967) 1312.CrossRefADSMathSciNetzbMATHGoogle Scholar
  21. 21.
    M. Karowski, Nucl. Phys. B153 (1979) 244.ADSCrossRefGoogle Scholar
  22. 22.
    I. V. Cherednik, Theor. Math. Phys. 61 (1984) 977.CrossRefMathSciNetzbMATHGoogle Scholar
  23. 23.
    I. V. Cherednik, Int. J. Mod. Phys. A7, Suppl. 1B (1992) 707.MathSciNetGoogle Scholar
  24. 24.
    S. Ghoshal and A. B. Zamolodchikov, Int. J. Mod. Phys. A9 (1994) 3841.CrossRefADSMathSciNetzbMATHGoogle Scholar
  25. 25.
    T. Inami and H. Konno, J. Phys. A27 (1994) 211.CrossRefMathSciNetGoogle Scholar
  26. 26.
    A. Fring and R. Köberle, Nucl. Phys. B421 (1994) 1592.CrossRefGoogle Scholar
  27. 27.
    R. Sasaki, Reflection Bootstrap Equations for Toda Field Theory, 1993. Preprint YITP/U-93-33.Google Scholar
  28. 28.
    F. C. Alcaraz, M. N. Barber, M. T. Batchelor, R. J. Baxter and G. R. W. Quispel, 1987, J. Phys. A: Math. Gen. 20 6397.CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    E. K. Sklyanin, J. Phys. A21 (1988) 2375CrossRefADSMathSciNetzbMATHGoogle Scholar
  30. 30.
    V. Pasquier and H. Saleur, Nucl. Phys. B330 (1990) 523CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    P. P. Kulish and E. K. Sklyanin, J. Phys. A24 (1991) L435.CrossRefADSMathSciNetGoogle Scholar
  32. 32.
    L. Mezincescu, R. I. Nepomechie and V. Rittenberg, Phys. Lett. A147 (1990) 70; L. Mezincescu, R. I. Nepomechie, J. Phys. A24 (1991) L17; Int. J. Mod. Phys. A6 (1991) 5231, ibid. Int. J. Mod. Phys. A7 (1992) 5657.CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    H. J. de Vega and A. González Ruiz, J. Phys. A26 (1993) L519.CrossRefGoogle Scholar
  34. 34.
    E. K. Sklyanin, Funct. Analy. Apply. 21 (1987) 164.CrossRefMathSciNetzbMATHGoogle Scholar
  35. 35.
    L. Pittner and P. Uray, J. Math. Phys. 36 (1995) 944.CrossRefADSMathSciNetzbMATHGoogle Scholar
  36. 36.
    M. Jimbo, R. Kedem, T. Kojima, M. Konno and T. Miwa, XXZ chain with boundary, Preprint RIMS, hep-th/9411121, 1994.Google Scholar
  37. 37.
    P. P. Kulish, Zap. Nauch. Semin. LOMI, 145 (1985) 140; J. Sov. Math. 35 (1986) 1111; Lett. Math. Phys. 10 (1985) 87.MathSciNetGoogle Scholar
  38. 38.
    H. M. Babujian and R. Flume, Mod. Phys. Lett. 9 (1994) 2029–2039CrossRefADSMathSciNetzbMATHGoogle Scholar
  39. 39.
    K. Hikami, P. P. Kulish and M. Wadati, J. Phys. Soc. Japan, 61 (1992) 3071–3081.CrossRefMathSciNetADSGoogle Scholar
  40. 40.
    P. P. Kulish, S. Rauch-Wojciechowski and A. V. Tsiganov, Mod. Phys. Lett., 9 (1994) 2063–2073.CrossRefADSMathSciNetzbMATHGoogle Scholar
  41. 41.
    E. K. Sklyanin, Comm. Math. Phys. 142 (1992) 123–132.MathSciNetGoogle Scholar
  42. 42.
    M. Karowski and A. Zapletal, Nucl. Phys. B419 (1994) 111.CrossRefMathSciNetGoogle Scholar
  43. 43.
    H. Grosse, S. Pallua, P. Prester and E. Raschhofer, J. Phys. A27 (1994) 4761–4771.CrossRefADSMathSciNetzbMATHGoogle Scholar
  44. 44.
    M. L. Ge and Q. Zhao, Phys. Lett. A175 (1993) 199.CrossRefMathSciNetGoogle Scholar
  45. 45.
    C. K. Lai, J. Math. Phys. 15 (1974) 954–956.CrossRefADSGoogle Scholar
  46. 46.
    V. B. Kuznetsov and A. V. Tsiganov, J. Phys. A22 (1989) L73–L79.CrossRefADSMathSciNetGoogle Scholar
  47. 47.
    E. Ogievetsky, N. Yu. Reshetikhin and P. B. Wiegmann, Nucl. Phys. B280 (1987) 45.CrossRefADSMathSciNetGoogle Scholar
  48. 48.
    V. Bazhanov, A. Schadrikov, Theor. Math. Phys. 73 (1987) 402.zbMATHGoogle Scholar
  49. 49.
    A. V. Zabrodin, Quantum transfer matrices for discrete and continuous quasiexactly solvable problems. Preprint HEP-TH-9412116, 1994.Google Scholar
  50. 50.
    P. P. Kulish, Zap. Nauch. Sem. LOMI, 109 (1981) 83; J. Sov. Math. 23 (1984) 2111.MathSciNetzbMATHGoogle Scholar
  51. 51.
    P. P. Kulish and R. Sasaki Prog. Theor. Phys. 89 (1993) 741.CrossRefADSMathSciNetGoogle Scholar
  52. 52.
    E. Cremmer and J.-L. Gervais, Comm. Math. Phys. 144 (1992) 279.CrossRefADSMathSciNetzbMATHGoogle Scholar
  53. 53.
    P. Martin and V. Rittenberg, Int. J. Mod. Phys. A7, Suppl. (1992) 707.CrossRefADSMathSciNetzbMATHGoogle Scholar
  54. 54.
    M. Karowski, Lect. Notes Phys. 380 (1990) 183.ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    L. Freided and J.-M. Maillet, Phys. Lett. B262 (1991) 278; ibid. B263 (1991) 403.CrossRefADSMathSciNetGoogle Scholar
  56. 56.
    M. L. Ge and H. C. Fu, J. Phys. A25 (1992) L1233CrossRefADSMathSciNetzbMATHGoogle Scholar
  57. 57.
    S. Lukyanov and Ya. Pugai, Bosonization of ZF algebras: direction toward deformed Virasoro algebra. Preprint RU-94-41, 1994.Google Scholar
  58. 58.
    M. Gaudin, J. Phys. France 49 (1988) 1857; Y. Shibukawa and K. Ueno, Lett. Math. Phys. 25 (1992) 239–248; P.P. Kulish and V.D. Lipovsky, Phys. Lett. A 127 (1988) 413.MathSciNetCrossRefGoogle Scholar
  59. 59.
    V. Rittenberg and D. Wyler, Nucl. Phys. B139 (1978) 189; M. Scheunert, J. Math. Phys. 24 (1983) 2671; D. Gurevich, Leningrad Math. J., 2 (1991) 801; D. S. McAnally, Lett. Math. Phys. 33 (1995) 249.CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • P. P. Kulish
    • 1
    • 2
  1. 1.Departmento de Física Teórica and IFICCentro Mixto Universidad de Valencia CSICBurjassot (Valencia)Spain
  2. 2.St. Peterburgs Branch of Steklov Mathematical Institute of the Russian Academy of ScienesSt. PetersburgRussia

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