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TMF, 2000, Volume 125, Number 2, Pages 179–204 (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)

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.

DOI: https://doi.org/10.4213/tmf663

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English version:
Theoretical and Mathematical Physics, 2000, 125:2, 1455–1475

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Received: 28.04.2000

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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\by A.~V.~Zabrodin
\paper Hidden quantum $R$-matrix in the discrete-time classical Heisenberg magnet
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\vol 125
\issue 2
\pages 179--204
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\jour Theoret. and Math. Phys.
\yr 2000
\vol 125
\issue 2
\pages 1455--1475
\crossref{https://doi.org/10.1007/BF02551007}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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