Group “Fundamental Interactions”
Our activities concern the mathematical description of physical laws, in particular those governing the fundamental interactions. The necessary tools are geometric, algebraic, combinatorial, or analytical in nature. Some problems lead to the emergence of new mathematical structures and require specific study. Others have immediate physical applications.
The laws of nature, at the classical level, are naturally expressed in geometric terms (the notion of a connection on a fiber bundle, for example, appears both in the formulation of the laws of gravitation and in those of the strong or electroweak interactions), and the symmetries of physics are described by constructions arising from group theory, in particular representation theory. Finally, it is well known that mechanics itself uses geometry—especially symplectic geometry—for its own formulation. At the quantum level, all these mathematical concepts must be generalized. Thus, approaches to quantum gravity using noncommutative geometry replace space-time (in fact the algebra of functions defined on it) with a noncommutative algebra, and many developments in quantum field theory use generalizations of the concept of a group: supersymmetric theories use Lie superalgebras, and conformal field theory, as well as string theory and integrable systems, relies on concepts from affine algebras and quantum groups. Our activities are focused on these themes.
| IOCHUM | Bruno | Research teacher emeritus | +33.4.91.26.97.95 | Contact |
| KRAJEWSKI | Thomas | Research teacher | +33.4.91.26.95.53 | Contact |
| LAZZARINI | Serge | Research teacher Team leader « Geometry, Physics, and Symmetries » | +33.4.91.26.97.94 | Contact |
| MASSON | Thierry | Researcher | +33.4.91.26.97.96 | Contact |
| OGIEVETSKY | Oleg | Research teacher emeritus | +33.4.91.26.95.33 | Contact |
| PORTELA | Leandre | Ph.D. | Contact | |
| TRIAY | Roland | Research teacher emeritus | +33.4.91.26.95.19 | Contact |
| USALA | Louis | Ph.D. | Contact |
Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory
Seminaire Lotharingien de Combinatoire, 2014, 70, pp.B70c
Conjugation properties of tensor product multiplicities
Journal of Physics A: Mathematical and Theoretical, 2014, 47, pp.455202. (10.1088/1751-8113/47/45/455202)
Polchinski's equation for group field theory
Fortschritte der Physik / Progress of Physics, 2014, 62 pp.855-862. (10.1002/prop.201400043)
Gauge field theories: various mathematical approaches
Eckstein, Michal; Heller, Michael; Szybka, Sebastian J. Mathematical Structures of the Universe, Copernicus Center Press, 2014, 978-83-7886-107-2
Conformal Carroll groups
Journal of Physics A: Mathematical and Theoretical, 2014, 47 (33), pp.335204. (10.1088/1751-8113/47/33/335204)
Proceedings, 14th International Symposium Frontiers of Fundamental Physics (FFP14): Marseille, France, July 15-18, 2014
Kajfasz, Eric; Masson, Thierry; Triay, Roland. Frontiers of Fundamental Physics 14, Jul 2014, Marseille, France. PoS, 2014
Polarized Spinoptics and Symplectic Physics
2013
Alternating subgroups of Coxeter groups and their spinor extensions
Journal of Pure and Applied Algebra, 2013, 217 (11), pp.2198-2211. (10.1016/j.jpaa.2013.02.007)
Gauge theories and generalized connections on transitive Lie algebroids
Mathematical Physics [math-ph]. Aix-Marseille Université, 2013. English. (NNT : )
Explicit metrics for a class of two-dimensional cubically superintegrable systems
Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics, Jul 2013, Marseille, France. pp.354-372, (10.1016/j.geomphys.2014.08.004)
