Skip to main content
European Commission logo print header
Contenu archivé le 2022-12-23

Correlation functions in integrable models of quantum field theory and their applications to phase transitions in low-dimensional systems

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 integrable
models of statistical mechanics and two-dimensional models with nontrivial spectral curves.

v. Developing the representation theory approach to quantum
integrability.

The main tasks of the project are:

1. Study of reductions of integrable models.
2. Study of the all-distance behaviour of correlation functions in
integrable 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 related
2-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 reductions
of different quantum integrable models.
2. New explicit formulas for form factors and vacuum expectation
values 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 for
which 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 model
and 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 manageable
form which allows direct applications in condensed matter physics.

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
Coût total
Aucune donnée

Participants (9)