Abstract:
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.
Citation:
A. N. Leznov, M. A. Mukhtarov, “Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain”, TMF, 71:1 (1987), 46–53; Theoret. and Math. Phys., 71:1 (1987), 370–375
\Bibitem{LezMuk87}
\by A.~N.~Leznov, M.~A.~Mukhtarov
\paper Internal symmetry algebra of exactly integrable dynamical systems in the quantum domain
\jour TMF
\yr 1987
\vol 71
\issue 1
\pages 46--53
\mathnet{http://mi.mathnet.ru/tmf4856}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=913922}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 71
\issue 1
\pages 370--375
\crossref{https://doi.org/10.1007/BF01029097}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1987K689200006}
Linking options:
https://www.mathnet.ru/eng/tmf4856
https://www.mathnet.ru/eng/tmf/v71/i1/p46
This publication is cited in the following 5 articles:
Alexander Zuevsky, “Affine Toda equations and solutions in the homogeneous grading”, Linear Algebra and its Applications, 542 (2018), 149
A. N. Leznov, “Graded Lie algebras, representation theory, integrable mappings, and integrable systems”, Theoret. and Math. Phys., 122:2 (2000), 211–228
Angel Ballesteros, Sergei M Chumakov, “On the spectrum of a Hamiltonian defined onsuq(2) and quantum optical models”, J. Phys. A: Math. Gen., 32:35 (1999), 6261
A. N. Leznov, “Integrable two-dimensional ultra-Toda mappings and chains”, Theoret. and Math. Phys., 117:1 (1998), 1194–1207
V Spiridonov, A Zhedanov, “Symmetry preserving quantization and self-similar potentials”, J. Phys. A: Math. Gen., 28:22 (1995), L589
Citation in format AMSBIB
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