Communications in Mathematical Physics

, Volume 171, Issue 3, pp 531–546 | Cite as

Particle-field duality and form factors from vertex operators

  • Costas Efthimiou
  • André LeClair
Article

Abstract

Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values of such vertex operators in the space of fields. The vertex operators can be constructed explicitly in radial quantization. Furthermore, these vertex operators can be exactly bosonized in momentum space. We develop these ideas by studying the free-fermion point of the sine-Gordon theory, and use this scheme to compute some form-factors of some non-free fields in the sine-Gordon theory. This work further clarifies earlier work of one of the authors, and extends it to include the periodic sector.

Keywords

Neural Network Statistical Physic Complex System Form Factor Nonlinear Dynamics 

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References

  1. 1.
    Zamolodchikov, A.B., Zamolodchikov, A.I.B.: Ann. Phys.120, 253 (1979)Google Scholar
  2. 2.
    Karowski, M., Weisz, P.: Nucl. Phys.B139, 445 (1978)Google Scholar
  3. 3.
    Smirnov, F.A.: Form Factors in Completely Integrable Models of Quantum Field Theory. In: Advanced Series in Mathematical Physics14, Singapore: World Scientific, 1992Google Scholar
  4. 4.
    Smirnov, F.A.: J. Phys. A. Math. Gen.19, L575 (1986)Google Scholar
  5. 5.
    LeClair, A.: Nucl. Phys.B415, 734 (1994)Google Scholar
  6. 6.
    Lukyanov, S.: Commun. Math. Phys.167, 183 (1995)Google Scholar
  7. 7.
    Lukyanov, S.: Phys. Lett.B325, 409 (1994)Google Scholar
  8. 8.
    Lukyanov, S., Shatashvili, S.: Phys. Lett.B298, 111 (1993)Google Scholar
  9. 9.
    Davies, B., Foda, O., Jimbo, M., Miwa, T., Nakayashiki, A.: Commun. Math. Phys.151, 89 (1993); Jimbo, M., Miki, K., Miwa, T., Nakayashiki, A.: Phys. Lett.A168, 256 (1992)Google Scholar
  10. 10.
    Unruh, W.G.: Phys. Rev.D14, 870 (1976) Unruh, W.G., Wald, R.M.: Phys. Rev.D29, 1047 (1984)Google Scholar
  11. 11.
    Fubini, S., Hanson, A.J., Jackiw, R.: Phys. Rev.D7, 1732 (1973)Google Scholar
  12. 12.
    Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Nucl. Phys.B241, 333 (1984)Google Scholar
  13. 13.
    Coleman, S.: Phys. Rev.D11, 2088 (1975)Google Scholar
  14. 14.
    Itoyama, H., Thacker, H.B.: Nucl. Phys.B320, 541 (1989)Google Scholar
  15. 15.
    Griffin, P.: Nucl. Phys.B334, 637Google Scholar
  16. 16.
    Schroer, B., Truong, T.T.: Nucl. Phys.B144, 80 (1978); Marino, E.C., Schroer, B., Swieca, J.A.: Nucl. Phys.B200, 473 (1982)Google Scholar
  17. 17.
    Ginsparg, P.: Les Houches Lectures, 1988. In: Fields, Strings and Critical Phenomena, Brézin, E., Zinn-Justin J., Eds. Amsterdam: North Holland, 1990Google Scholar
  18. 18.
    Abdalla, E., Abdalla, M.C.B., Sotkov, G., Stanishkov, M.: Off Critical Current Algebras. Univ. Sao Paulo preprint. IFUSP-preprint-1027, Jan. 1993Google Scholar
  19. 19.
    Bernard, D., LeClair, A.: Commun. Math. Phys.142, 99 (1991); Phys. Lett.B247, 309 (1990)Google Scholar
  20. 20.
    Frenkel, I.B., Reshetikhin, N.Yu.: Commun. Math. Phys.146, 1 (1992)Google Scholar
  21. 21.
    Smirnov, F.A.: Int. J. Mod. Phys.A7, Suppl. IB, 813 (1992)Google Scholar
  22. 22.
    Frenkel, I.B., Jing, N.: Proc. Natl. Acad. Sci. USA85, 9373 (1988)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Costas Efthimiou
    • 1
  • André LeClair
    • 1
  1. 1.Newman LaboratoryCornell UniversityIthacaUSA

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