Form factors in \(D_n^{(1)}\) affine Toda field theories. (English) Zbl 0934.81067
Summary: We derive closed recursion equations for the symmetric polynomials occurring in the form factors of \(D_n^{(1)}\) affine Toda field theories. These equations follow from kinematical and bound state residue equations for the full form factor. We also discuss the equations arising from second- and third-order forward channel poles of the \(S\)-matrix. The highly symmetric case of \(D_4^{(1)}\) form factors is treated in detail. We calculate explicitly cases with a few particles involved.
MSC:
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 05E05 | Symmetric functions and generalizations |
| 81T10 | Model quantum field theories |
References:
| [1] | Smirnov, F. A., Form factors in completely integrable models of quantum field theory, (Adv. Series in Math. Phys., 14 (1992), World Scientific: World Scientific Singapore) · Zbl 0788.46077 |
| [2] | Karowski, M.; Weisz, P., Nucl. Phys. B, 139, 455 (1978) |
| [3] | Cardy, J. L.; Mussardo, G., Nucl. Phys. B, 340, 387 (1990) |
| [4] | Yurov, V. P.; Zamolodchikov, Al. Z., Int. J. Mod. Phys. A, 6, 3419 (1991) |
| [5] | Zamolodchikov, Al. Z., Nucl. Phys. B, 348, 619 (1991) |
| [6] | Koubek, A.; Mussardo, G., Phys. Lett. B, 311, 193 (1993) |
| [7] | Fring, A.; Mussardo, G.; Simonetti, P., Nucl. Phys. B, 393, 413 (1993) · Zbl 1245.81238 |
| [8] | Fring, A.; Mussardo, G.; Simonetti, P., Phys. Lett. B, 307, 83 (1993) |
| [9] | Delfino, G.; Mussardo, G., Phys. Lett. B, 324, 40 (1994) |
| [10] | Koubek, A., Nucl. Phys. B, 428, 655 (1994) · Zbl 1049.81629 |
| [11] | Delfino, G.; Mussardo, G., Nucl. Phys. B, 455, 724 (1995) · Zbl 0925.82042 |
| [12] | Oota, T., Nucl. Phys. B, 466, 361 (1996) · Zbl 1002.81518 |
| [13] | Kac, V., Infinite-dimensional Lie algebras (1990), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0716.17022 |
| [14] | Braden, H. W.; Sasaki, R., Phys. Lett. B, 255, 343 (1991) |
| [15] | Braden, H. W.; Corrigan, E.; Dorey, P. E.; Sasaki, R., Nucl. Phys. B, 338, 689 (1990) · Zbl 1029.81504 |
| [16] | Braden, H. W.; Corrigan, E.; Dorey, P. E.; Sasaki, R., Nucl. Phys. B, 356, 469 (1991) |
| [17] | Dorey, P., Nucl. Phys. B, 374, 741 (1992) · Zbl 0992.81521 |
| [18] | Destri, C.; De Vega, H. J., Nucl. Phys. B, 358, 251 (1991) |
| [19] | Niedermaier, M. R., Nucl. Phys. B, 424, 184 (1994) · Zbl 0866.35115 |
| [20] | T. Oota, private communication.; T. Oota, private communication. |
| [21] | C. Acerbi, G. Mussardo and A. Valeriani, preprint SISSA-105-96-EP, hep-th/9609080.; C. Acerbi, G. Mussardo and A. Valeriani, preprint SISSA-105-96-EP, hep-th/9609080. |
| [22] | MacDonald, I. G., Symmetric functions and Hall polynomials (1995), Clarendon Press: Clarendon Press Oxford · Zbl 0899.05068 |
| [23] | Vilenkin, N. Ja.; Klimyk, A. U., Representations of Lie Groups and Special Functions, Recent Advances (1995), Kluwer: Kluwer Dordrecht · Zbl 0826.22001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
