Geodesic
Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain
Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 1, pp. 46-53 
A. N. Leznov; M. A. Mukhtarov. Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain. Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 1, pp. 46-53. http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a5/
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     title = {Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown on the example of the generalized Toda chain in two-dimensional space that semisimple algebras of a classical problem turn in the quantum region into associative Hopf algebras described in Drinfeld's paper as quantum algebras. In terms of quantum algebras the Heisenberg operators of interacting field as functions of the in-fields are expressed by the classical theory formulas and the expressions for them obtained earlier get a simple algebraical meaning.

[1] Leznov A. N., Fedoseev I. A., TMF, 53:3 (1982), 358–373 | MR

[2] Fedoseev I. A., Leznov A. N., Phys. Lett., 141B:1–2 (1984), 100–103 | DOI | MR

[3] Drinfeld V. G., DAN SSSR, 283:5 (1985), 1060–1064 | MR | Zbl

[4] Inoni E., Wigner E. P., Proc. Acad. Sci. USA, 39 (1956), 510–518 | DOI

[5] Leznov A. N., Group Theoret. Methods in Phys., Gordon and Breach, N. Y., 1984

[6] Leznov A. N., Smirnov V. G., Shabat A. B., TMF, 51:1 (1982), 10–21 | MR | Zbl