Team 4 Physics Mathematics 

Our team is generally interested in the following topics

1) Develop and treat precisely and analytically certain fundamental problems of physics in the presence of external interactions within the framework of relativistic and non-relativistic quantum mechanics. The working method would be to solve equations of relativistic particles (spinorial, tensorial) in a rigorous mathematical framework: for the cases
- systems depend on time
- the framework of deformed algebras
- in the context of non-commutative geometry etc….
A parallel step, of course, would be to study Quantum Field Theory with its two versions Feynman and Schwinger in the framework of deformed algebras, despite the feat of its experimental predictions, it remains riddled with divergences that we have not yet can only be eliminated by methods, mathematical regularization and physical renormalization. Furthermore, with the developments of new theories, it turns out that the deformation approach is one which is best prepared for explicit calculations and the generalization of this quantum field theory to be able to include the gravitational field and it would be profitable to see the way in which this deformation influences the properties of causality and locality of the fields and then it would be better to re-study the analytic properties of the relative Green functions, to re-deduce Feynman's diagrammatics and to see the profound changes brought by this deformation to these methods of regularization and renormalization, gift of seeing
- Study of divergences in quantum field theory in the context of deformed algebras,
- Revision of the ambiguities of quantum field theory and clarification of their nature in this deformation framework.
- Study using the methods of quantum field theory, physics which involves intense external fields and determination of the phenomena of the creation of pairs.
- Study of this quantum field theory in the limiting case of relativistic wave equations in the presence of deformation
2)Path integral is a quantification method closely linked to classical physics. This formalism based on the Lagrangian has borne fruit in quantum theory and proves to be a very suitable mathematical method in the case of perturbative development. Its extension to the case of deformed spaces (geometrically and algebraically) would be interesting for calculating the propagators involved in relativistic quantum mechanics and quantum field theory. Of course, we will be interested in the calculation of this path integral in the non-relativistic case in the presence of potentials (as an interaction model) and in the relativistic case in the presence of external fields.
3) Show the existence and uniqueness of the classical solution of certain linear and non-linear fractional evolution problems with nonlocal type boundary conditions (integral) from physics, the demonstration is based on a priori estimates and the density of the image of the operator generated by the problem considered, then we apply some numerical or semi-analytical methods for ulistration,

Running as of 31/12/2018