DIADEMS: Developing an Integrable Approach to Dynamical and Elliptic ModelS
The participants of this Project met in a natural way around a problematic aimed at covering both the physical and mathematical aspects of integrable systems. They are respectively members of two mathematical physics groups from two physics laboratories and two physical mathematics group of two mathematical departments. The four groups have a worldwide expertise in integrable systems, especially in elliptical and dynamical models where they have produced in common a number of significant publications. It must also be emphasized that several PhD students were already trained with mutual participation of members of the proposal. They have afterwards successively joined various international research teams.
The Project intends to build on this expertise so as to get a very rich and efficient team tackling the development of the theory of elliptic and dynamical algebras, and integrable systems associated to such structures. Several aspects will be studied during the Project, each of the problems being defined so as to lead to both mathematical and physical advances. Indeed, the new framework introduced for the mathematical study of elliptic and/or dynamical structures will allow us to define and to solve new (or up-to-now unsolved) physical models. As an illustration, the study of Manin matrices (that we propose to extend to the elliptic case) has already triggered the construction of new higher Gaudin Hamiltonians. In the same way, the elaboration of new quantum dynamical algebras is expected to yield new Ruijsenaars-Schneider type models. As a last example, the calculation of scalar products of Bethe vectors defined through the projection method should provide an efficient way of computing correlation functions in spin chain models.