Geodesic
Functional tetrahedron equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 370-384 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_1998_117_3_a3,
     author = {R. M. Kashaev and I. G. Korepanov and S. M. Sergeev},
     title = {Functional tetrahedron equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {370--384},
     year = {1998},
     volume = {117},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a3/}
}
TY  - JOUR
AU  - R. M. Kashaev
AU  - I. G. Korepanov
AU  - S. M. Sergeev
TI  - Functional tetrahedron equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1998
SP  - 370
EP  - 384
VL  - 117
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a3/
LA  - ru
ID  - TMF_1998_117_3_a3
ER  - 
%0 Journal Article
%A R. M. Kashaev
%A I. G. Korepanov
%A S. M. Sergeev
%T Functional tetrahedron equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1998
%P 370-384
%V 117
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a3/
%G ru
%F TMF_1998_117_3_a3
R. M. Kashaev; I. G. Korepanov; S. M. Sergeev. Functional tetrahedron equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 370-384. http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a3/

[1] V. V. Bazhanov, Yu. G. Stroganov, TMF, 52 (1982), 105–113 | MR

[2] J. Hietarinta, J. Phys. A, 27 (1994), 5727–5748 ; Labeling schemes for tetrahedron equations and dualities between them, E-print hep-th/9402139 | DOI | MR | Zbl

[3] I. G. Korepanov, Algebraic integrable dynamical systems, $(2+1)$-dimensional models in wholly discrete space-time, and inhomogeneous models in $2$-dimensional statistical physics, , 1995 E-print solv-int/9506003

[4] S. M. Sergeev, Solutions of the functional tetrahedron equation connected with the local Yang–Baxter equation for the ferro-electric, E-print solv-int/9709006 | MR

[5] R. M. Kashaev and S. M. Sergeev, Commun. Math. Phys., 195 (1998), 309–319 ; On pentagon, ten-term, and tetrahedron relations, E-print q-alg/9607032 | DOI | MR | Zbl

[6] R. M. Kashaev, Lett. Math. Phys., 35 (1996), 389–397 ; On discrete 3-dimensional equations associated with the local Yang–Baxter relation, E-print solv-int/9512005 | DOI | MR

[7] T. Miwa, Proc. Japan Acad. Ser. A, 58 (1982), 9–12 | DOI | MR | Zbl

[8] I. G. Korepanov, Integrability in $3+1$ dimensions: relaxing a tetrahedron relation, E-print solv-int/9712006