Skip to main content
Log in

Calculation of norms of Bethe wave functions

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

A class of two dimensional completely integrable models of statistical mechanics and quantum field theory is considered. Eigenfunctions of the Hamiltonians are known for these models. Norms of these eigenfunctions in the finite box are calculated in the present paper. These models include in particular the quantum nonlinear Schrödinger equation and the HeisenbergXXZ model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bethe, H.: Z. Phys.71, 205–226 (1931)

    Google Scholar 

  2. Yang, C.N., Yang, C.P.: Phys. Rev.150, 321–327 (1966)

    Google Scholar 

  3. Lieb, E.H.: Phys. Rev. Lett.18, 692–694 (1967)

    Google Scholar 

  4. Berezin, F.A., Pokhil, C.P., Finkelberg, V.M.: Vestn. Mosk. Gos. Univ. Ser.1.1, 21–28 (1964)

    Google Scholar 

  5. McGuire, J.B.: J. Math. Phys.5, 622–636 (1964);

    Google Scholar 

  6. Brézin, E., Zinn-Justin, J.: C.R. Acad. Sci. Paris263, 670–673 (1966);

    Google Scholar 

  7. Gaudin, M.: J. Math. Phys.12, 1674–1676, 1677–1680 (1971)

    Google Scholar 

  8. Faddeev, L.D.: Sov. Sci. Rev. Math. Phys. C1, 107–160 (1981)

    Google Scholar 

  9. Faddeev, L.D., Takhtajan, L.A.: Usp. Mat. Nauk34, 13–63 (1979)

    Google Scholar 

  10. Gaudin, M.: Preprint, Centre d'Etudes Nucleaires de Saclay, CEA-N-1559, (1), (1972)

  11. Gaudin, M., McCoy, B.M., Wu, T.T.: Phys. Rev. D23, 417–419 (1981)

    Google Scholar 

  12. Baxter, R.J.: J. Stat. Phys.9, 145–182 (1973)

    Google Scholar 

  13. Izergin, A.G., Korepin, V.E.: Lett. Math. Phys. (to be published)

  14. Faddeev, L.D., Sklyanin, E.K.: Dokl. Akad. Nauk SSSR243, 1430–1433 (1978)

    Google Scholar 

  15. Sklyanin, E.K.: Dokl. Akad. Nauk SSSR244, 1337–1341 (1978)

    Google Scholar 

  16. Izergin, A.G., Korepin, V.E., Smirnov, F.A.: Teor. Mat. Fiz.48, 319–323 (1981)

    Google Scholar 

  17. Sklyanin, E.K.: Zap. Nauchn. Seminarov LOMI95, 55–128 (1980)

    Google Scholar 

  18. Izergin, A.G., Korepin, V.E.: Dokl. Akad. Nauk SSSR259, 76–79 (1981)

    Google Scholar 

  19. Izergin, A.G., Korepin, V.E.: Nucl. Phys. B, Field Theory and Statistical Systems B205 [FS5], 401–413 (1982)

    Google Scholar 

  20. Izergin, A.G., Korepin, V.E.: Lett. Math. Phys.5, 199–205 (1981)

    Google Scholar 

  21. Baxter, R.J.: Stud. Appl. Math.L50, 51–67 (1971)

    Google Scholar 

  22. Belavin, A.A.: Phys. Lett. B87, 117–121 (1980)

    Google Scholar 

  23. Kulish, P.P.: Physica D3, 246–257 (1981)

    Google Scholar 

  24. Faddeev, L.D., Takhtajan, L.A.: Zap. Nauchn. Seminarov LOMI109, 134–178 (1981)

    Google Scholar 

  25. Baxter, R.J.: Philos. Trans. Soc. London, Ser. A289, 315–346 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korepin, V.E. Calculation of norms of Bethe wave functions. Commun.Math. Phys. 86, 391–418 (1982). https://doi.org/10.1007/BF01212176

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01212176

Keywords

Navigation