Sergeev, S. M. Quantum \(2+1\) evolution model. (English) Zbl 0962.81023 J. Phys. A, Math. Gen. 32, No. 30, 5693-5714 (1999). Summary: A quantum evolution model in \(2+1\) discrete spacetime, connected with a 3D fundamental map \(\mathbb{R}\), is investigated. Map \(\mathbb{R}\) 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 \(\mathbb{R}\)-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 belp of the current system. Thus, the complete integrability in 3D is proved directly. Cited in 12 Documents MSC: 81R12 Groups and algebras in quantum theory and relations with integrable systems PDFBibTeX XMLCite \textit{S. M. Sergeev}, J. Phys. A, Math. Gen. 32, No. 30, 5693--5714 (1999; Zbl 0962.81023) Full Text: DOI arXiv