### Abstract

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 language | English |
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Pages (from-to) | 5693-5714 |

Number of pages | 22 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 32 |

Issue number | 30 |

DOIs | |

Publication status | Published - 30 Jul 1999 |

Externally published | Yes |

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### Cite this

*Journal of Physics A: Mathematical and General*,

*32*(30), 5693-5714. https://doi.org/10.1088/0305-4470/32/30/313

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*Journal of Physics A: Mathematical and General*, vol. 32, no. 30, pp. 5693-5714. https://doi.org/10.1088/0305-4470/32/30/313

**Quantum 2 + 1 evolution model.** / Sergeev, S. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum 2 + 1 evolution model

AU - Sergeev, S. M.

PY - 1999/7/30

Y1 - 1999/7/30

N2 - 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.

AB - 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.

KW - quantum evolution model

UR - http://www.scopus.com/inward/record.url?scp=0033618195&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/32/30/313

DO - 10.1088/0305-4470/32/30/313

M3 - Article

VL - 32

SP - 5693

EP - 5714

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 30

ER -