Professor Vladimir Bazhanov
Position 
Head of Department 

Department 
Department of Theoretical Physics 
Office phone 
55500 
Email 

Office 
Le Couteur 3 11 
Mathematical Aspects of Conformal Field Theory
Conformal Field Theory (CFT) in twodimensions describes physics of the second order transitions in statistical mechanics and also plays important role in string theory, which is expected to unify the theory of strong interaction with quantum gravity. The project aims to explore and further develop mathematical techniques of CFT.
Exact BohrSommerfeld quantisation and Conformal Field Theory
It is well known that the quasiclassical quantisation of the harmonic oscillator leads to its exact quantum mechanical spectrum. Remarkably, this result can be generalized to various anharmonic systems via mysterious connections to Conformal Field Theory.
New connections between classical and quantum field theories
The standard correspondence principle implies that quantum theory reduces to classical theory in the limit of the vanishing Planck constant. This project is devoted to a new type connection between quantum and classical systems which holds for arbitrary finite values of the Planch constant.
Combinatorics and integrable systems
We will study links between integrable systems in statistical mechanics, combinatorial problems and special functions in mathematics. This area of research has attracted many scientist's attention during the last decade and revealed unexpected links to other areas of mathematics like enumeration problems and differential equations.
High energy scattering in gauge and string theories
It appears that the scattering amplitudes in Quantum Chromodynamics (theory of strong interactions) can be exactly calculated in certain limiting cases (e.g. in the socalled multiRedge kinematics). This is possible due to remarkable connections of this problem to the theory of integrable systems based on the YangBaxter equation.
String theory and integrable systems
This project aims to develop and employ the full power of the theory of integrable quantum systems to new models of quantum manybody spin systems in string theory.
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