On quantum $L$-operator for two-dimensional lattice Toda model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 87-99 Cet article a éte moissonné depuis la source Math-Net.Ru

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The two-dimensional quantum lattice Toda model for the affine and simple Lie algebras of the type A is considered. For its known $L$-operator a correction of the second order in the lattice parameter $\varepsilon$ is found. It is proved that the equation determining a correction of the third order in $\varepsilon$ has no solutions.
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A. G. Bytsko; I. Yu. Davydenkova. On quantum $L$-operator for two-dimensional lattice Toda model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 87-99. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a4/

[1] A. V. Mikhailov, “Ob integriruemosti dvumernogo obobscheniya tsepochki Toda”, Pisma v ZhETF, 30 (1979), 443–448

[2] A. N. Leznov, M. A. Saveliev, “Representation of zero curvature for the system of nonlinear partial differential equations $\chi_{\alpha z\bar z}=(\exp K\chi)_\alpha$ and its integrability”, Lett. Math. Phys., 3 (1979), 489–494 | DOI | MR | Zbl

[3] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[4] O. Babelon, H. J. de Vega, C. M. Viallet, “Solutions of the factorization equations from Toda field theory”, Nucl. Phys. B, 190 (1981), 542–552 | DOI | MR

[5] M. Jimbo, “Quantum $R$-matrix for the generalized Toda system”, Commun. Math. Phys., 102 (1986), 537–547 | DOI | MR | Zbl

[6] N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, Korrelyatsionnye funktsii integriruemykh sistem i kvantovyi metod obratnoi zadachi, Nauka, M., 1992 | MR | Zbl

[7] P. P. Kulish, N. Yu. Reshetikhin, “Kvantovaya lineinaya zadacha dlya uravneniya sinus-Gordon i vysshie predstavleniya”, Zap. nauchn. semin. LOMI, 101, 1981, 101–110 | MR

[8] L. D. Faddeev, O. Tirkkonen, “Connections of the Liouville model and XXZ spin chain”, Nucl. Phys. B, 453 (1995), 647–669 | DOI | MR | Zbl

[9] A. Aghamohammadi, M. Khorrami, A. Shariati, “Toda theories as contractions of affine Toda theories”, Phys. Lett. B, 389 (1996), 260–263 | DOI | MR