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Affine lie algebras in massive field theory and form factors from vertex operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 430-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the $q$-deformed affine $\widehat {sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie algebra split into two independent affine algebras on this factorized space, each with level 1 in the anti-periodic sector, and level 0 in the periodic sector. The space of fields in the anti-periodic sector can be organized using level-$1$ highest weight representations, if one supplements the ${\widehat {sl(2)}}$ algebra with the usual local integrals of motion. Introducing a particle-field duality leads to a new way of computing form-factors in radial quantization. Using the integrals of motion, a momentum space bosonization involving vertex operators is formulated. Form-factors are computed as vacuum expectation values of vertex operators in momentum space. 
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     author = {A. LeClair},
     title = {Affine lie algebras in massive field theory and form factors from vertex operators},
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A. LeClair. Affine lie algebras in massive field theory and form factors from vertex operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 3, pp. 430-441. http://geodesic.mathdoc.fr/item/TMF_1994_98_3_a11/

[1] A. B. Zamolodchikov, Al. B. Zamolodchikov, Annals Phys., 120 (1979), 253 | DOI | MR

[2] D. Bernard, A. LeClair, Commun. Math. Phys., 142 (1991), 99 ; Phys. Lett. B, 247 (1990), 309 | DOI | MR | Zbl | DOI | MR

[3] G. Felder, A. LeClair, Infinite analysis, part A, B (Kyoto, 1991), Adv. Ser. Math. Phys., 16, World Sci. Publ., 1992, 239–278 | MR

[4] F. A. Smirnov, Progr. Theoret. Phys. Suppl., 1992, no. 110, 329–335 | DOI | MR

[5] A. LeClair, Spectrum Generating Affine Lie Algebras in Massive Quantum Field Theory, CLNS 93/1220

[6] S. Coleman, Phys. Rev. D, 11 (1975), 2088 | DOI

[7] R. K. Kaul, R. Rajaraman, Int. J. Mod. Phys. A, 8 (1993), 1815 | DOI | MR

[8] E. Abdalla, M. C. B. Abdalla, G. Sotkov, M. Stanishkov, Off Critical Current Algebras, Univ. Sao Paulo preprint ; IFUSP-preprint-1027, jan. 1993 | MR

[9] S. Fubini, A. J. Hanson, R. Jackiw, Phys. Rev. D, 7 (1973), 1732 | DOI

[10] H. Itoyama, H. B. Thacker, Nucl. Phys. B, 320 (1989), 541 | DOI | MR

[11] P. Griffin, Nucl. Phys. B, 334, 637 | DOI | MR

[12] C. Efthimiou, A. LeClair Particle-Field Duality and Form-Factors from Vertex Operators, Comm. Math. Phys., 171:3 (1995), 531–546 | DOI | MR | Zbl

[13] B. Schroer, T. T. Truong, Nucl. Phys. B, 144 (1978), 80 ; E. C. Marino, B. Schroer, J. A. Swieca, Nucl. Phys. B, 200 (1982), 473 | DOI | MR | DOI | MR

[14] F. A. Smirnov, Form Factors in Completely Integrable Models of Quantum Field Theory, Advanced Series in Mathematical Physics, 14, World Scientific, 1992 | DOI | MR | Zbl

[15] S. Lukyanov, Free Field Representation for Massive Integrable Models, Rutgers preprint RU-93-30 | MR