Quantum 2 + 1 evolution model

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27 Citations (Scopus)


A quantum evolution model in 2 + 1 discrete spacetime, connected with a 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a 2D linear lattice system called 'the current system'. In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical and it corresponds to the known operator-valued R-matrix. The current system is a type of the linear problem for the 2 + 1 evolution model. A generating function for the integrals of motion for the evolution is derived with the help of the current system. Thus, the complete integrability in 3D is proved directly.

Original languageEnglish
Pages (from-to)5693-5714
Number of pages22
JournalJournal of Physics A: Mathematical and General
Issue number30
Publication statusPublished - 30 Jul 1999
Externally publishedYes


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