Homepage of Sergey Sergeev

Qualification

MSc, Theoretical Physics, 1989, Moscow State University

PhD, Theoretical Physics, 1993, Institute for High Energy Physics

Adv. PhD (Habilitation), Mathematics and Mathematical Physics, 2002, St-Petersburg Department of Steklov Institute of Mathematics

Contact Details

Department of Theoretical Physics

Research School of Physical Sciences and Engineering

Canberra ACT 0200, Australia

office 3.13 of Le Couteur building

phone + 61 2 6125 1002

facsimile + 61 2 6125 4676

e-mail Sergey.Sergeev

another e-mail Sergey.Sergeev

Course 2008: Relaivistic Quantum Mechanics

Lecture notes Relativistic quantum mechanics by R. J. Crewther

Lecture notes Advanced quantum mechanics by F. J. Dyson

Research Interests

My research interest is what is called Mathematical Physics. Basically it is an interest to the Mechanics - Classical, Statistical and especially Quantum. The subject of the research is many-body mechanical systems which can be solved explicitly - so called Exactly Integrable Systems. Importance of exact solution is that qualitative (e.g. critical) phenomena can not be obtained by a perturbation approximation. Quantum integrable systems with infinitely large number of degrees of freedom (i.e. integrable quantum field theories) have essential importanse for Physics. A huge class of such systems consist on «quantum chains» and «spin shains» - the theory critical properties of polymers and magnetics. My main expertise and dominant research interest  embraces the newest area of multidimensional quantum integrable systems - quantum lattices and spin lattices - yet this area is not developed well. Expertise and research interests include a variety of subjects underlying the theory of exact integrability: (mathematics) Yang-Baxter equation, Tetrahedron equation, general simplex equations, quantum groups, representation theory, algebraic geometry, differential equations, (physics) quantum field theory, integrable field theory, condensed matter physics and so on.

• S. Sergev, Adv. PhD thesis (not in English): Completely integrable models in three dimensional discrete space-time (ps-file here)

Lecture notes

Symmetry Groups and Algebras in Physics 2007

Methods of Mathematical Physics MATH3322

Introduction to Lie algebras and their representation theory MATH3349

Student projects

Hamiltonian hierarchies in 2+1 dimensional classical integrable models

Excitation spectrum for a spin lattice

Three or more projects related to three dimensional integrable models

Selected recent papers:

• S. Sergeev, Evolution operator for a quantum pendulum, Theoretical and Mathematical Physics, 138 (2004) 28-32
• S. Sergeev, Quantization scheme for modular q-difference equations, Theoretical and Mathematical Physics, 142 (2005)
• S. 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) 1055-1115. Russian version here
• S. Pakuliak and S. Sergeev, Quantum relativistic Toda chain at root of unity..., International Journal of Mathematics and Mathematical Sciences 31 (2002) 513-553
• V. Bazhanov and S. Sergeev, Zamolodchikov tetrahedron equation and hidden structure of quantum groups, J. Phys. A: Math. Gen. 39 (2006) 3295–3310
• S. Sergeev, Thermodynamic Limit for a Spin Lattice, Journal of Statistical Physics 123 (2006) 1231-1250
• S. Sergeev, Ansatz of Hans Bethe for a two-dimensional lattice Bose gas, J. Phys. A: Math. Gen. 39 (2006) 3035–3045
• S. Sergeev, Quantum curve in q-oscillator model, International Journal of Mathematics and Mathematical Sciences (2006) DOI 10.1155/IJMMS/2006/92064
• V. Bazhanov, V. Mangazeev, S. Sergeev, Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• V. Bazhanov, V. Mangazeev, S. Sergeev, Quantum geometry of 3-dimensional lattices

Recent research report

• S. M. Sergeev, V. V. Bazhanov, New solutions of Tetrahedron Equation
• S. Sergeev, q-oscillator lattice and representations of quantum groups
• S. Sergeev, Thermodynamic Limit of Spin Lattice
• S. Sergeev, Tetrahedron equation and Integrability
• S. Sergeev, Evolution operators and quantum chains
• S. Sergeev, Lectures on Multidimensional Integrability (Workshop and Summer School From Statistical Mechanics to Conformal and Quantum Field Theory, Melbourne 2007): Lecture 1, Lecture 2, Lecture 3
• S. Sergeev, On quantum geometry of 3d lattices

My Publication list

Waikato!

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