Objectif The purpose of this project is to develop the theory of quantum integrable models. This includes models of quantum mechanics, quantum field theory and statistical mechanics. These models have many important applications, among the most important ones are string theory and the theory of phase transitions. The present status of the theory allows the calculation of correlation functions, although the techniques are not yet as efficient as one would like to have them. The main objectives of the project are:i. Study of correlation functions in integrable models of quantum field theory and statistical mechanics over the whole range of distances.ii. Study of symmetry algebras, spaces of states, and correlation functions in conformal field theory.iii. Study of symmetry algebras of quantum integrable models.iv. Construction and classification of three-dimensional integrablemodels of statistical mechanics and two-dimensional models with nontrivial spectral curves.v. Developing the representation theory approach to quantumintegrability.The main tasks of the project are:1. Study of reductions of integrable models.2. Study of the all-distance behaviour of correlation functions inintegrable models.3. Design of a general method for the exact computation of correlation functions of quantum integrable models.4. Study of conformal field theory and current algebras.5. Applications of conformal field theory to string theory.6. Study of dualities in two-dimensional integrable quantum field theories.7. Formulation and investigation of new 3-dimensional and related2-dimensional lattice integrable models.8. Study of relations between semigroups and integrable stochastic models.9. Quantum integrability and representation theory.The main expected results are:1. Systematic description of the spaces of states for reductionsof different quantum integrable models.2. New explicit formulas for form factors and vacuum expectationvalues of local operators in integrable quantum field theories.Methods to study the all-distance behavior of correlation functions.3. New families of solvable conformal field theories.4. Generalizations of the Gepner and Kazama-Suzuki models of string theory which include D-branes and their solutions.5. Lagrangian description of some families of integrable models forwhich the scattering data is given.6. New explicit solutions of 3-dim tetrahedron and tetrahedron reflection equations.7. Functional Bethe ansatz for the non-homogeneous Chiral Potts modeland its parametrization in terms of theta-functions on a higher genus algebraic curves.8. Construction of the universal integrable system associated to the moduli space of G-bundles over algebraic curves.9. Method to obtain physical correlation functions in a manageableform which allows direct applications in condensed matter physics. Programme(s) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Thème(s) OPEN - OPEN Call Appel à propositions Data not available Régime de financement Data not available Coordinateur RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITÄT BONN Contribution de l’UE Aucune donnée Adresse Nussallee 12 BONN Allemagne Voir sur la carte Liens Site web Opens in new window Coût total Aucune donnée Participants (9) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire ECOLE NORMALE SUPÉRIEURE DE LYON France Contribution de l’UE Aucune donnée Adresse ALLÉE D'ITALIE, 46 LYON Voir sur la carte Coût total Aucune donnée Instititute of Theoretical and Experimental Physics Russie Contribution de l’UE Aucune donnée Adresse Bolshaya Cheremushkinskaya 26 117259 Moscow Voir sur la carte Coût total Aucune donnée Joint Institute of Nuclear Research Russie Contribution de l’UE Aucune donnée Adresse Jolio Curie 6 141980 Dubna, Moscow region Voir sur la carte Coût total Aucune donnée National Academy of Ukraine Bogolyubov Institute of Theoretical Physics Ukraine Contribution de l’UE Aucune donnée Adresse Metrologicheskaya 14b 03143 Kiev Voir sur la carte Coût total Aucune donnée Russian Academy of Science Landau Institute for Theoretical Physics Russie Contribution de l’UE Aucune donnée Adresse Institutski prospekt 14 142432 Chernogolovka, Moscow region Voir sur la carte Coût total Aucune donnée Russian Academy of Science Steklov Mathematical Institute Russie Contribution de l’UE Aucune donnée Adresse Gubkina 8 119991 Moscow Voir sur la carte Coût total Aucune donnée Universite Pierre et Marie Curie France Contribution de l’UE Aucune donnée Adresse Place Jussieu 4 75252 CEDEX 05 Paris Voir sur la carte Coût total Aucune donnée Universite de Bourgogne France Contribution de l’UE Aucune donnée Adresse avenue Alain Savary 9 21079 Dijon Voir sur la carte Coût total Aucune donnée Universite de Montpellier II France Contribution de l’UE Aucune donnée Adresse Place E. Batalion 34095 CEDEX 05 Montpellier Voir sur la carte Coût total Aucune donnée