The analysis of relativistic quantum systems

Relativistic Quantum Mechanics is central in Physics and Mathematical Physics. It plays a very important role in the analysis of many relevant topics in that field. The basic operator for relativistic models is the Dirac operator. Contrary to the case of the non-relativistic Schrödinger operator, the Dirac operator is not semi-bounded, its spectrum being real and unbounded in both directions, for positive and negative values having a gap (−m, m), m the mass of the particle, in the middle of the essential spectrum. This property has many consequences, both for the physical interpretation of the solutions of the models based on the Dirac operator as for the much more difficult mathematical analysis of those models. These difficulties arise already at the level of one-particle systems. For N-particle systems, the difficulties arising from the total unboundedness of the operator together with the usual difficulties for N-particle systems in Quantum Mechanics are very stimulating mathematically, since they are the source of a large number of very interesting and difficult problems that are far from being understood at the moment. Various groups of mathematicians and mathematical physicists have specialized on these topics in the past two or three decades and have produced already a good amount of important results. But much remains to be understood and proved. The aim of this workshop is to stimulate the interaction of researchers in all those groups, researchers who have different approaches, points of view and methodologies. Also many of them have so far specialized on a part of the theory, and open discussions about the models, the difficulties to analyze them, the existing methods, the new perspectives to tackle more difficult problems out of reach at the moment, among all of them should be a great opportunity for making progress and opening new perspectives for the future.