Quantum 2 + 1 evolution model

Journal of Physics A: Mathematical and General

Volumn 32, Issue 30, 1999, Pages 5693-5714

  Sergeev, S M ^a  

^a Branch Institute for Nuclear Physics   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033618195     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/30/313     Document Type: Article

References (32)

1. Zamolodchikov A B 1981 Tetrahedron equations and the relativistic S matrix of straight strings in 2+1 dimensions Commun. Math. Phys. 79, 489-505
2. Bazhanov V V and Stroganov Yu G 1982 D-simplex equation Teor. Mat. Fiz. 52 105-13
3. Baxter R J 1986 The Yang-Baxter equations and the Zamolodchikov model Physica D 18 321-47
4. Bazhanov V V and Baxter R J 1992 New solvable lattice models in three dimensions J. Stat. Phys. 69 453-85
5. Sergeev S M, Mangazeev V V and Stroganov Yu G 1996 The vertex formulation of the Bazhanov-Baxter model J. Stat. Phys. 82
6. Faddeev L D and Volkov A Yu 1997 Algebraic quantization of integrable models in discrete space-time Preprint hep-th/9710039
7. Kashaev R M and Reshetikhin N Yu 1997 Affine Toda field theory as 2 + 1 dimansional integrable system Commun. Math. Phys. 188 251-66
8. Korepanov I G 1995 Algebraic integrable dynamical systems, 2 + 1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics Preprint solv-int/9506003
9. Korepanov I G 1997 'Some eigenstates for a model associated with solutions of tetrahedron equation I-V Preprint solv-int/9701016, 9702004, 9703010, 9704013, 9705005
10. Korepanov I G 1997 Particles and strings in a 2 + 1-D integrable quantum model Preprint solv-int/9712006 Commun. Math. Phys. submitted
11. Baxter R J 1983 On Zamolodchikov's solution of the Tetrahedron equations Commun. Math. Phys. 88 185-205
12. Mangazeev V V, Kashaev R M and Stroganov Yu G 1993 Star-square and Tetrahedron equations in the Baxter-Bazhanov model Int. J. Mod. Phys. A 8 1399-409
13. Korepanov I G 1993 Tetrahedral Zamolodchikov algebras corresponding to Baxter's L-operators Commun. Math. Phys. 154 85-97
14. Maillet J-M and Nijhoff F W 1990 Multidimensional lattice integrability and the simplex equations Proc. Como Conf. on Nonlinear Evolution Equations: Integrability and Spectral Methods ed A Degasperis, A P Fordy and M Lakshmanan (Manchester: Manchester University Press) pp 537-48
15. Maillet J-M and Nijhoff F W 1989 Integrability for multidimensional lattice models Phys. Lett. B 224 389-96
16. Maillet J-M 1990 Integrable systems and gauge theories Nucl. Phys. (Proc. Suppl.) B 18 212-41
17. Faddeev L and Volkov A Yu 1994 Hirota equation as an example of an integrable symplectic map Lett. Math. Phys. 32 125-35
18. Sergeev S M 1998 Lett. Math. Phys. 45 113-19 (Sergeev SM 1997 Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric Preprint solv-int/9709006)
19. Sergeev S M 1998 Lett. Math. Phys. 45 113-19 (Sergeev SM 1997 Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric Preprint solv-int/9709006)
20. Sergeev S M 1997 On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation Preprint solv-int/9709013 Int. J. Mod. Phys. A to appear
21. Sergeev S M 1999 Phys. Lett. A 253 145-50 (Sergeev S M 1998 3D symplectic map Preprint solv-int/9802014)
22. Sergeev S M 1999 Phys. Lett. A 253 145-50 (Sergeev S M 1998 3D symplectic map Preprint solv-int/9802014)
23. Sergeev S M 1996 Operator solutions of simplex equations Proc. X Int. Conf. Problems of Quantum Field Theory (Alushta, 1996) (Moscow: Joint Institute for Nuclear Research) pp 154-7
24. Sergeev S M Maillard J-M 1997 Three dimensional integrable models based on modified Tetrahedron equations and quantum dilogarithm Phys. Lett. B 405 55-63
25. Faddeev L D and Kashaev R M 1994 Quantum dilogarithm Mod. Phys. Lett. A 9
26. Bazhanov V V and Reshetikhin N Yu 1995 Remarks on the quantum dilogarithm J. Phys. A: Math. Gen. 28 2217
27. Faddeev L D 1995 Discrete Heisenberg-Weyl group and modular group Lett. Math. Phys. 34 249-54
28. Bazhanov V V, Sergeev S M and Mangazeev V V 1995 Quantum dilogarithm and the Tetrahedron equation Preprint IHEP 95-141
29. Sergeev S M 1997 Two-dimensional R-matrices-descendants of three dimensional R-matrices Mod. Phys. Lett. A 12 1393-410
30. Korepanov I G, Kashaev R M and Sergeev S M 1998 Functional tetrahedron equation Preprint solv-int/9801015 TMF to appear
31. Kashaev R M and Sergeev S M 1998 On pentagon, ten-term, and tetrahedron relations Commun. Math. Phys. 195 309-19
32. Sergeev S M 1998 Preprint solv-int/9811003