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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 125, Number 2, Pages 179–204
DOI: https://doi.org/10.4213/tmf663 (Mi tmf663) 		 
Hidden quantum $R$-matrix in the discrete-time classical Heisenberg magnet

A. V. Zabrodinab

a N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
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DOI: https://doi.org/10.4213/tmf663
Abstract: We construct local $M$-operators for an integrable discrete-time version of the classical Heisenberg magnet by convoluting the twisted quantum trigonometric $4\times4$ $R$-matrix with certain vectors in its “quantum” space. Components of the vectors are identified with $\tau$-functions of the model. Hirota's bilinear formalism is extensively used. The construction generalizes the known representation of $M$-operators in continuous-time models in terms of Lax operators and the classical $r$-matrix.
Received: 28.04.2000
English version:
Theoretical and Mathematical Physics, 2000, Volume 125, Issue 2, Pages 1455–1475
DOI: https://doi.org/10.1007/BF02551007
Bibliographic databases:
Language: Russian
Citation: A. V. Zabrodin, “Hidden quantum $R$-matrix in the discrete-time classical Heisenberg magnet”, TMF, 125:2 (2000), 179–204; Theoret. and Math. Phys., 125:2 (2000), 1455–1475
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
     
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