Publications

SERGEY M. SERGEEV

A) Published refereed journal articles, chronological order

1. S. M. Sergeev, Spectral Decomposition of R – Matrices for Exceptional Lie Algebras. Modern Phys. Lett. A 6 (1991) pp 923 – 927

2. S. M. Sergeev, E8 Level 2 RSOS Model. Modern Phys. Lett. A6 (1991) pp 2335 – 2344

3. A. V. Batunin, S. M. Sergeev, Transfer Matrix Method and Intermittence generating Dynamics in Hadron Physics. Phys. Lett. B327 (1994) pp 293 – 300

4. S. M. Sergeev, G. G. Volkov, The Non-Abelian Gauge Family Symmetry in the Four Dimensional Free Fermion Super-string Approach. Rus. J. of Nucl. Phys. (Yad. Fiz.) 57 N. 1 (1994) pp 168 – 174

5. A. A. Maslikov, S. M. Sergeev, G. G. Volkov, Grand Unified String Theories with SU(3) Gauge Family Symmetry. Phys. Lett. B328 (1994) pp 319 – 328

6. A. A. Maslikov, S. M. Sergeev, G. G. Volkov, The Grand Unified String Theories with Non – Abelian Gauge Family Symmetry in Free Fermion Formulation. Physical Review D50 (1994) pp 7440-7449

7. A. A. Maslikov, S. M. Sergeev, G. G. Volkov, String Motivated Grand Unified Theories with Horizontal Gauge Symmetry. Int. J. of Mod. Phys. A9 (1994) pp 5369-5385

8. V. V. Mangazeev, S. M. Sergeev, Yu. G. Stroganov, New Series of 3D Lattice Integrable Models. Int. J. of Mod. Phys. A9 (1994) pp 5517-5530

9. H. E. Boos, V. V. Mangazeev, S. M. Sergeev, Modified Tetrahedron Equations and Related 3D Integrable Models. Int. J. of Mod. Phys. A10 (1995)

10. V. V. Mangazeev, S. M. Sergeev, Yu. G. Stroganov, New solution of vertex type tetrahedron equations. Mod. Phys. Lett. A10 (1995) pp 279-287

11. S. M. Sergeev, V. V. Mangazeev and Yu. G. Stroganov, Vertex reformulation of the Bazhanov – Baxter model. J. Stat. Phys. 82 (1996) pp 31 – 50

12. S. M. Sergeev, H. E. Boos, V. V. Mangazeev and Yu. G. Stroganov, $\Psi$ – vectors for three-dimensional models. Mod. Phys. Lett. A11 (1996) pp 491-498

13. J.-M. Maillard, I. G. Korepanov and S. M. Sergeev, Classical Limit for a 3D Lattice Spin Model. Physic Letters A 232 (1997) pp 211 – 216

14. J.-M. Maillard, S. M. Sergeev, Three dimensional integrable models based on modified tetrahedron equations and quantum dilogarithm. Physics Letters B 405 (1997) pp 55 – 63

15. S. M. Sergeev, Two-dimensional R-matrices – descendants of three-dimensional R-matrices. Mod. Phys. Lett. A 12 (1997) pp 1393 – 1410

16. R. M. Kashaev, S. M. Sergeev, On pentagon, ten-term, and tetrahedron relations. Commun. Math. Phys. 195 (1997) pp 211-216

17. S. M. Sergeev, Solutions of the functional tetrahedron equation connected with the local Yang – Baxter equation for the ferro-electric condition. Lett. Math. Phys. 45 (1998) pp 113-119

18. S. M. Sergeev, 3D symplectic map. Phys. Lett. A 253 (1999) pp 145-150

19. S. M. Sergeev, A three-dimensional integrable quantum mapping. Theoretical and Mathematical Physics 118 (1999) pp 479-487

20. S. M. Sergeev, Solitons in a 3d integrable model. Phys. Lett. A 265 (2000) pp 364-368

21. R. M. Kashaev, I. G. Korepanov and S. M. Sergeev, Functional Tetrahedron Equation. Theoretical and Mathematical Physics 117 (1998) pp 370-384

22. S. M. Sergeev, Quantum 2 + 1 evolution model. J. Phys. A: Math. Gen. 32 (1999) pp 5693-5714

23. S. M. Sergeev, On exact solution of a classical 3D integrable model. J. Nonlinear Math. Phys. 1 (2000) pp 57-72

24. S. M. Sergeev, Auxiliary transfer matrices for three-dimensional integrable models. Theoretical and Mathematical Physics 124 (2000) pp 391-409

25. S. M. Sergeev, Quantum matrices of the coefficients of a discrete linear problem. (Russian) Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 269 No. 16 (2000) Vopr. Kvant. Teor. Polya i Stat. Fiz. 292-307, 370-371
Translation: Coefficient Matrices of a Quantum Discrete Auxiliary Linear Problem. Journal of Mathematical Sciences 115(1) (2003) pp 2049-2057

26. S. Sergeev, Integrable three-dimensional models in wholly discrete space-time. Integrable structures of exactly solvable two-dimensional models of quantum field theory (Kiev, 2000) NATO Sci. Ser. II Math. Phys. Chem. 35 (2001) 293/304 Kluwer Acad. Publ.

27. S. Sergeev, Complex of three-dimensional solvable models. J. Phys. A: Math. Gen. 34 (2001) pp 10493-10503

28. G. Pronko and S. Sergeev, Quantum relativistic Toda chain. J. Appl. Math. 1 (2001) pp 47-68

29. V. V. Mangazeev and S. M. Sergeev, The continuous limit of the triple $\tau$-function model. Theoretical and Mathematical Physics 129 (2001) pp 317-326

30. G. P. Pronko and S. M. Sergeev, Q-operators for the simple quantum relativistic Toda chain. Phys. Atomic Nuclei 65 (2002) pp 1095-1099

31. S. Pakuliak and S. Sergeev, Quantum relativistic Toda chain at root of unity: invariant approach. Czechoslovak J. Phys. 51 (2001) pp 1414-1419

32. S. Pakuliak and S. Sergeev, Quantum relativistic Toda chain at root of unity: isospectrality, modified Q-operator, and functional Bethe Ansatz. Int. J. Math. Math. Sci. 31 (2002) pp 513-553

33. G. von Gehlen, S. Pakuliak and S. Sergeev, Explicit free parameterization of the modified tetrahedron equation. J. Phys. A: Math. Gen. 36 (2003) pp 975-998

34. A. P. Isaev and S. M. Sergeev, Quantum Lax operators and discrete 2+1-dimensional integrable models, Lett. Math. Phys. 64 (2003) pp 57-64

35. S. Z. Pakuliak and S. M. Sergeev, Spectral Curves and Parameterization of a Discrete Integrable Three Dimensional Model, Theoretical and Mathematical Physics 136 (2003) pp 917-935

36. S. M. Sergeev, Functional equations and quantum separation of variables for 3d spin models. Theoretical and Mathematical Physics 138 (2004) pp 226-237

37. G. von Gehlen, S. Pakulyak and S. Sergeev, The modified tetrahedron equation and its solutions, Int. J. Mod. Phys. A19S2 (2004) pp 179-204

38. S. Pakuliak, S. Sergeev, G. v. Gehlen, Theta function parameterization and fusion for 3-D integrable Boltzmann weights. J. Phys. A: Mathe. Gen 37(2004) pp 1159-1179

39. S. M. Sergeev, Evidence for a phase transition in three dimensional lattice models. Theoretical and Mathematical Physics 138 (2004) pp 310-321

40. S. M. Sergeev, Evolution operator for a quantum pendulum. Theoretical and Mathematical Physics 138 (2004) pp 28-32

41. S. M. Sergeev, Quantization scheme for modular q-difference equations. Theoretical and Mathematical Physics 142 (2005) pp 422-430

42. S. M. Sergeev, Quantum integrable models in discrete 2+1 dimensional space-time: auxiliary linear problem on a lattice, zero curvature representation, isospectral deformation of the Zamolodchikov-Bazhanov-Baxter model. Particles and Nuclei 35 (2004) pp 1051-1111.

43. G. von Gehlen, S. Pakuliak and S. Sergeev, Bazhanov-Stroganov model from 3D approach. J. Phys. A: Math. Gen. 38 (2005) pp 7269-7298

44. S. M. Sergeev, Thermodynamic limit for a spin lattice. Journal of Statistical Physics 123 1231-1250 (2006)

45. V. Bazhanov and S. Sergeev, Zamolodchikov’s tetrahedron Equation and Hidden Structure of Quantum Groups, J. Phys. A: Math. Gen. 39 (2006) pp 3295-3310

46. S. Sergeev, Integrability of q-oscillator lattice model. Physics Letters A 357 (2006) pp 417-419

47. S. Sergeev, Quantum curve in q-oscillator model. International Journal of Mathematics and Mathematical Sciences (2006) DOI 10.1155/IJMMS/2006/92064

48. S. Sergeev, Ansatz of Hans Bethe for a two-dimensional Bose gas. J. Phys. A: Math. Gen. 39 (2006) pp 3035-3045

49. M. Bortz and S. Sergeev, The q-deformed Bose gas: integrability and thermodynamics. Eur. Phys. J. B 51 (2006) pp 395-405

50. S. Sergeev, Evolution operators for quantum chains. J. Phys. A: Math. Theor. 40 (2007) pp F209-F213

51. V. V. Bazhanov, V. V. Mangazeev and S. M. Sergeev, Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry. Nuclear Physics B 784 [FS] (2007) pp 234–258

52. S. Sergeev, Quantization of three-wave equations. J. Phys. A: Math. Theor. 40 (2007) pp 12709–12724

53. V. V. Bazhanov, V. V. Mangazeev and S. M. Sergeev, Exact solution of the Faddeev-Volkov model, Phys. Lett. A 372 (2008) pp 1547—1550

54. S. M. Sergeev, Tetrahedron equations and nilpotent subalgebras of Uq(sln), Lett. Math. Phys. 83 (2008) pp 231-235

55. V. Bazhanov, V. Mangazeev and S. Sergeev, Quantum geometry of three dimensional lattices, J. Stat. Mech. (2008) P07004

56. S. Sergeev, Tetrahedron equations, boundary states and hidden structure of Uq(Dn). J. Phys. A: Math. Theor. 42 (2009) 082002

57. S. Sergeev, Geometry of quadrilateral nets: Second Hamiltonian form. Journal of Geometry and Physics, 59 (2009) 1150-1154.

58. S. Sergeev, Super-tetrahedra and super-algebras, Journal of Mathematical Physics 50 (2009) to appear in August.

59. S. Sergeev, Classical Integrable Field Theories in Discrete 2+1 dimensional space-time. J. Phys. A: Math. Theor. 42 (2009) 295206

60. S. Sergeev, Ground states of the Heisenberg evolution operator in discrete three-dimensional spacetime and quantum discrete BKP equations. J. Phys. A: Math. Theor. 42 (2009) 295207

B) Refereed conference proceedings

1. V. V. Mangazeev, S. M. Sergeev and Yu. G. Stroganov, The tetrahedron equation and three-dimensional integrable models. Proceeding of Geometry and Integrable models, eds. Pyatov P. N., Solodukhin S. N., World Scienti.c Publishing Co., 1994, pp 3-19.

2. S. M. Sergeev, V. V. Bazhanov, H. E. Boos, V. V. Mangazeev and Yu. G. Stroganov, Tetrahedron equation for pedestrians. Proceedings of the HEP and QFT Conference, Zvenigorod, September 1995.

3. V. V. Mangazeev, Yu. G. Stroganov and S. M. Sergeev, The Tetrahedron Equation and its Solutions. Resent Progress in Statistical Mechanics and Quantum Field Theory, eds. P. Bouwknegt, P. Fendley, J. Minahan, D. Nemschansky, K. Pilch, H. Saleur and N. P. Warner, World Scienti.c Publishing Co., 1995, pp. 255 – 270.

4. S. M. Sergeev, V. V. Mangazeev, G. E. Boos and Yu. G. Stroganov, Introduction into tetrahedron equation. Proceedings of the Theoretical Physics Conference, ITEP, Moscow, June 1995.

5. S. M. Sergeev, V. V. Mangazeev, G. E. Boos and Yu. G. Stroganov, Vertex – IRF duality in three dimensions. Proceedings of the Conference on Mathematical Physics, Chelyabinsk, July 1995.

6. H. E. Boos, V. V. Mangazeev, S. M. Sergeev, Modified tetrahedron equation and related 3D models. Proceedings of XX International Colloquium on Group Theoretical Methods in Physics, Tonoyaka, World Scientific Publishing Co., 1995, pp. 314-319.

7. S. M. Sergeev, Operator solutions of simplex equations. Proc. X Int. Conf. Problems of Quantum Field Theory (Alushta, 1996) (Moscow: Joint Institute for Nuclear Research, ed. A. Vladimirov) pp. 154-157

8. G. von Gehlen, S. Pakuliak and S. Sergeev, 3-dimensional integrable lattice models and the Bazhanov-Stroganov model. Nankai Tracts in Math. 10: Differential Geometry and Physics, ed. Mo-Lin Ge and Weiping Zhang, World Scientific, Singapore Dec.2006

C) Preprints and papers submitted for publications

1. A. V. Batunin and S. M. Sergeev, Second order quadratic mapping, Preprint BINP 96 – 01

2. S. M. Sergeev, $Z_N^{\otimes n}$- Broken Model. Preprint IHEP 92 – 07

3. S. M. Sergeev, Statistical Mechanics for $Z_N^{\otimes n}$-Broken Model. Preprint IHEP 92 – 46

4. S. M. Sergeev, V. V. Bazhanov and V. V. Mangazeev, Quantum Dilogarithm and Tetrahedron Equation. Preprint IHEP 95 – 129

5. S. M. Sergeev, On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation. Preprint solv-int/9709013

6. I. G. Korepanov and S. M. Sergeev, Eigenvector and eigenvalue problem for 3D bosonic model. Preprint solv-int/9802014

7. S. Sergeev, Completely integrable discrete systems in three dimensional space-time. Adv PhD thesis, S. Petersburg Division of Mathematical Institute (2001) (in Russian), available at http://tpsrv.anu.edu.au/Members/sergeev

8. S. Pakuliak and S. Sergeev, Relativistic Toda chain at root of unity. Preprint ITEP TH-86/00 (2000) and nlin.SI/0101024 (2001)

9. S. Pakuliak and S. Sergeev, Relativistic Toda chain at root of unity II. Modified Q-operator. Preprint MPI 2001 – 65 and nlin.SI/0107062 (2001)

10. S. Pakuliak and S. Sergeev, Relativistic Toda chain at root of unity III. Relativistic Toda chain hierarchy. Preprint MPI 2001 – 66 and nlin.SI/0107063 (2001)

11. S. Sergeev, Mathematics of quantum integrable systems in multidimensional discrete space-time, a monograph in preparation, preliminary version available on http://staff.estem-uc.edu.au/mathphysics.

12. S. Sergeev and P. Vassiliou, Hamiltonian Flows for Modified Discrete Three-Wave System, in preparation.

13. S. Sergeev and P. Vassiliou, PDE-Involution and hierarchy of Hamiltonians for Three-Wave Equations, in preparation.