# Functional tetrahedron equation

R. M. Kashaev, I. G. Korepanov, S. M. Sergeev

Research output: Contribution to journalArticle

28 Citations (Scopus)

### 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.

Original language English 1402-1413 12 Theoretical and Mathematical Physics 117 3 https://doi.org/10.4213/tmf939 Published - Dec 1998 Yes

### Fingerprint

Triangular pyramid
tetrahedrons
Integrable Models
Block Matrix
Matrix Models
Quantization
Space-time
Symmetry
symmetry
matrices
Model
Form

### Cite this

Kashaev, R. M., Korepanov, I. G., & Sergeev, S. M. (1998). Functional tetrahedron equation. Theoretical and Mathematical Physics, 117(3), 1402-1413. https://doi.org/10.4213/tmf939
Kashaev, R. M. ; Korepanov, I. G. ; Sergeev, S. M. / Functional tetrahedron equation. In: Theoretical and Mathematical Physics. 1998 ; Vol. 117, No. 3. pp. 1402-1413.
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Kashaev, RM, Korepanov, IG & Sergeev, SM 1998, 'Functional tetrahedron equation', Theoretical and Mathematical Physics, vol. 117, no. 3, pp. 1402-1413. https://doi.org/10.4213/tmf939

Functional tetrahedron equation. / Kashaev, R. M.; Korepanov, I. G.; Sergeev, S. M.

In: Theoretical and Mathematical Physics, Vol. 117, No. 3, 12.1998, p. 1402-1413.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Functional tetrahedron equation

AU - Kashaev, R. M.

AU - Korepanov, I. G.

AU - Sergeev, S. M.

PY - 1998/12

Y1 - 1998/12

N2 - 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.

AB - 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.

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JF - Theoretical and Mathematical Physics(Russian Federation)

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Kashaev RM, Korepanov IG, Sergeev SM. Functional tetrahedron equation. Theoretical and Mathematical Physics. 1998 Dec;117(3):1402-1413. https://doi.org/10.4213/tmf939