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 |