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Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory


Unification of approaches is a recent trend in the theory of exactly solvable models. Interrelations between different methods, such as form factor bootstrap, vertex operator approach and QISM have been found which indicate the existence of a common origin for different integrable structures. New powerful methods have been developed. So it seems that it is the right time to solve the following long-standing problems:

i. To develop a systematic and unified approach to the calculation of various quantities of physical importance (vacuum expectation values of local operators, correlation functions, form factors) for different types of exactly solvable models of quantum field theory, including models with higher genera spectral curves and models in strong coupling regimes;

ii. To investigate the structure of spaces of states of different models focusing on the `fermionic' structures that are displayed in the so called `fermionic' formulas for characters, including the classification of excitations in a finite volume;

iii. To investigate solvable models of quantum field theory in a finite volume at finite temperatures, including models with boundaries and boundary interactions.

The main tasks of the project are:

1. Development of the generalized Fourier transform method;
2. Investigation of the `fermionic' structure of spaces of states;
3. Investigation of the chiral Potts and related models;
4. To obtain expectation values of local fields in massive models of quantum field theory;
5. Investigation of massive quantum field theories in finite volume and for finite temperatures;
6. Development of methods for the calculation of correlation functions.
The main expected results are:

1. The description of the spectra and wave functions of a number of exactly solvable models, including the relativistic Toda chain, chiral Potts model and Sergeev's 2+1 dimensional model;
2. Clarifying the `fermionic' structure of spaces of states in conformal field theory and lattice models;
3. Correlation functions and form factors of models of quantum field theory and lattice models, including finite-volume and finite-temperature corrections to form factors and correlation functions;
4. Vacuum expectation values of local bulk and boundary operators in models of quantum field theory.

Though the teams develop different approaches and their favourite models are sometimes different, their efforts are directed to the solution of the same problem: the description of spaces of states and the calculation of correlation functions. The collaboration will allow the groups to work more effectively and to find more relations between different approaches and models.


Universität Bonn
Nussallee 12
53115 Bonn

Participants (7)

Institute of Theoretical and Experimental Physics
Bolshaya Cheremushkinskaya 25
117259 Moscow
Joint Institute for Nuclear Research
Jolio Curie,6
141980 Dubna, Moscow Region
National Academy of Sciences of Ukraine
Metrologicheskaya 14B
252143 Kiev
Russian Academy of Sciences
Institutski Prospekt 14
142432 Chernogolovka, Moscow District
Universite de Montpellier II
Place E. Batalion
34095 CEDEX 05 Montpellier
Université Pierre et Marie Curie
Place Jussieu 4
75252 Paris Cedex 05
Université de Bourgogne
Avenue Alain Savary 9
21078 Dijon