This article is cited in 61 papers

Functional tetrahedron equation

R. M. Kashaev^a, I. G. Korepanov^b, S. M. Sergeev<sup>c

a</sup> St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
^b South Ural State University
^c Branch of the Institute of Nuclear Physics

Abstract: We describe a method for constructing classical integrable models in a $(2+1)$-dimensional discrete space–time 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.

Received: 28.02.1998

DOI: 10.4213/tmf939

 English version: Theoretical and Mathematical Physics, 1998, 117:3, 1402–1413

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