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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_1987_71_1_a5,
     author = {A. N. Leznov and M. A. Mukhtarov},
     title = {Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {46--53},
     year = {1987},
     volume = {71},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a5/}
}
TY  - JOUR
AU  - A. N. Leznov
AU  - M. A. Mukhtarov
TI  - Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1987
SP  - 46
EP  - 53
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a5/
LA  - ru
ID  - TMF_1987_71_1_a5
ER  - 
%0 Journal Article
%A A. N. Leznov
%A M. A. Mukhtarov
%T Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1987
%P 46-53
%V 71
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a5/
%G ru
%F TMF_1987_71_1_a5
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/

[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