Vacuum curves and classical integrable systems in 2+1 discrete dimensions
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A dynamical system in discrete time is studied by means of algebraic geometry. This system has reductions which can be interpreted as classical field theory in the 2+1 discrete space-time. The study is based on the technique of vacuum curves and vacuum vectors. The evolution of the system has hyperbolic character, i.e., has a finite propagation speed. Bibliography: 10 titles.
KeywordsDynamical System Field Theory Discrete Time Integrable System Algebraic Geometry
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- 1.R. J. Baxter,Ann. Phis.,76, 1–24 (1973).Google Scholar
- 4.L. A. Takhtajan and L. D. Faddeev,Usp. Mat. Nauk,34:5, 13–63 (1979).Google Scholar
- 5.I. G. Korepanov,Vacuum Curve of the L-Operators Connected with 6-Vertex Model, and Construction of the R-Operators [in Russian], Chelyabinsk, Dep. in the VINITI, No. 2271-V86 (1986).Google Scholar
- 6.I. G. Korepanov,Applications of Algebraic-Geometric Constructions to the Triangle and Tetrahedron Equations [in Russian], Leningrad, (1990).Google Scholar
- 7.I. G. Korepanov,Hidden Symmetries of the 6-Vertex Model [in Russian], Chelyabinsk, Dep. in VINITI No. 1472-V87 (1987).Google Scholar
- 8.I. G. KorepanovOn the Spectrum of the 6-Vertex Model Transfer Matrix [in Russian], Chelyabinsk, Dep. in VINITI No. 3268-V87 (1987).Google Scholar
- 9.I. G. Korepanov,New Solutions to the Tetrahedron Equation [in Russian], Chelyabinsk, Dep. in VINITI No. 1751-V89 (1989).Google Scholar
- 10.M. P. Bellon, J.-M. Maillard, and C.-M. Viallet, “Higher dimensional mappings”, Preprint (1991).Google Scholar