Quantum 2+1 Evolution Model
نویسنده
چکیده
A quantum evolution model in 2+1 discrete space – time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system called “the current system”. In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical one and it corresponds to known operator-valued R – matrix. The current system is a kind of the linear problem for 2 + 1 evolution model. A generating function for the integrals of motion for the evolution is derived with a help of the current system. The subject of the paper is rather new, and so the perspectives of further investigations are widely discussed. PACS: 05.50; 02.10; 02.20. Mathematics Subject Classifications (1991): 47A60, 47A67, 22D25.
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