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Functional tetrahedron equation

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Abstract

We describe a method for constructing classical integrable models in a (2+1)-dimensional discrete spacetime based on the functional tetrahedron equation, an equation that makes the symmetries of a model obvious in a local form. We construct a very general “block-matrix model,” find its algebraic-geometric solutions, and study its various particular cases. We also present a remarkably simple quantization scheme for one of those cases.

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Authors and Affiliations

  1. St. Petersburg Branch, steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191011, St. Petersburg, Russia

    R. M. Kashaev

  2. South Ural State University, Ave. Lenin, 76, 454080, Chelyabinsk, Russia

    I. G. Korepanov

  3. Branch Institute for Nuclear Physics, 142284, Protvino, Russia

    S. M. Sergeev

Authors
  1. R. M. Kashaev
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  2. I. G. Korepanov
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  3. S. M. Sergeev
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Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 370–384, December, 1998.

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Kashaev, R.M., Korepanov, I.G. & Sergeev, S.M. Functional tetrahedron equation. Theor Math Phys 117, 1402–1413 (1998). https://doi.org/10.1007/BF02557179

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  • DOI: https://doi.org/10.1007/BF02557179

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