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.
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Zamolodchikov, A.B., Zamolodchikov, A.I.B.: Ann. Phys.120, 253 (1979)
Karowski, M., Weisz, P.: Nucl. Phys.B139, 445 (1978)
Smirnov, F.A.: Form Factors in Completely Integrable Models of Quantum Field Theory. In: Advanced Series in Mathematical Physics14, Singapore: World Scientific, 1992
Smirnov, F.A.: J. Phys. A. Math. Gen.19, L575 (1986)
LeClair, A.: Nucl. Phys.B415, 734 (1994)
Lukyanov, S.: Commun. Math. Phys.167, 183 (1995)
Lukyanov, S.: Phys. Lett.B325, 409 (1994)
Lukyanov, S., Shatashvili, S.: Phys. Lett.B298, 111 (1993)
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)
Unruh, W.G.: Phys. Rev.D14, 870 (1976) Unruh, W.G., Wald, R.M.: Phys. Rev.D29, 1047 (1984)
Fubini, S., Hanson, A.J., Jackiw, R.: Phys. Rev.D7, 1732 (1973)
Belavin, A.A., Polyakov, A.M., Zamolodchikov, A.B.: Nucl. Phys.B241, 333 (1984)
Coleman, S.: Phys. Rev.D11, 2088 (1975)
Itoyama, H., Thacker, H.B.: Nucl. Phys.B320, 541 (1989)
Griffin, P.: Nucl. Phys.B334, 637
Schroer, B., Truong, T.T.: Nucl. Phys.B144, 80 (1978); Marino, E.C., Schroer, B., Swieca, J.A.: Nucl. Phys.B200, 473 (1982)
Ginsparg, P.: Les Houches Lectures, 1988. In: Fields, Strings and Critical Phenomena, Brézin, E., Zinn-Justin J., Eds. Amsterdam: North Holland, 1990
Abdalla, E., Abdalla, M.C.B., Sotkov, G., Stanishkov, M.: Off Critical Current Algebras. Univ. Sao Paulo preprint. IFUSP-preprint-1027, Jan. 1993
Bernard, D., LeClair, A.: Commun. Math. Phys.142, 99 (1991); Phys. Lett.B247, 309 (1990)
Frenkel, I.B., Reshetikhin, N.Yu.: Commun. Math. Phys.146, 1 (1992)
Smirnov, F.A.: Int. J. Mod. Phys.A7, Suppl. IB, 813 (1992)
Frenkel, I.B., Jing, N.: Proc. Natl. Acad. Sci. USA85, 9373 (1988)
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Communicated by R.H. Dijkgraaf
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Efthimiou, C., LeClair, A. Particle-field duality and form factors from vertex operators. Commun.Math. Phys. 171, 531–546 (1995). https://doi.org/10.1007/BF02104677
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DOI: https://doi.org/10.1007/BF02104677