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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Examples of Hamiltonian structures in the theory of integrable models, and their quantization

Author: L. D. Faddeev
Translated by: M. A. Semenov-Tyan-Shanskiĭ
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 295-302
MSC (2010): Primary 81S05, 81S10, 81S20; Secondary 37K10
Published electronically: March 12, 2014
MathSciNet review: 3114855
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Abstract: A brief survey of certain important examples mentioned in the title and certain quantization methods.

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Additional Information

L. D. Faddeev
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

Keywords: Hamiltonian structure, quantization, Poisson bracket, Abelian current, Liouville model, Magri bracket, discretization, modular double
Received by editor(s): January 20, 2013
Published electronically: March 12, 2014
Additional Notes: Partially supported by RFBR (grants nos. 11-01-00570 and 11-01-12037) and by the RAS program “Mathematical problems of nonlinear dynamics”
Dedicated: To the memory of Vladimir Buslaev
Article copyright: © Copyright 2014 American Mathematical Society