×

zbMATH — the first resource for mathematics

On integrability of the Yang-Baxter \(\sigma\)-model. (English) Zbl 1215.81099
Summary: We prove that the recently introduced Yang-Baxter \(\sigma\)-model can be considered as an integrable deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution of the deformed model. With the help of this map, the standard procedure of the dressing of the principal chiral solutions can be directly transferred into the deformed Yang-Baxter context.

MSC:
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.)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
81R12 Groups and algebras in quantum theory and relations with integrable systems
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] DOI: 10.1007/s002200050256 · Zbl 0908.35107
[2] DOI: 10.1088/0305-4470/39/41/S17 · Zbl 1105.81306
[3] DOI: 10.1088/1126-6708/2002/12/051
[4] DOI: 10.1007/978-3-663-14092-4_7
[5] Semenov-Tian-Shansky, M. Dressing Transformations and Poisson Groups Actions, Publications of the RIMS Vol. 21 (Kyoto University, Kyoto, 1985), p. 1237. · Zbl 0673.58019
[6] DOI: 10.1016/S0370-2693(96)01468-2
[7] DOI: 10.1088/1126-6708/2006/10/012
[8] Uhlenbeck K., J. Diff. Geom. 30 pp 1– (1989)
[9] Zakharov V. E., Sov. Phys. JETP 47 pp 1017– (1978)
[10] Zhelobenko D. P., Translations of Mathematical Monographs 40, in: Compact Lie Groups and Their Representations (1973)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.