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 |
Analyticity results for the cumulants in a random matrix model
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2015, 2 (2), pp.169-228. (10.4171/AIHPD/17)
Residual Weyl symmetry out of conformal geometry and its BRST structure
Journal of High Energy Physics, 2015, 09, pp.195. (10.1007/JHEP09(2015)195)
The history of the universe is an elliptic curve
2014
Reduction of gauge symmetries: a new geometrical approach
Mathematical Physics [math-ph]. Aix-Marseille Université, 2014. English. (NNT : )
On the cosmological constant: its identification as renormalization group invariant scale corresponding to a gravitational condensate
Frontiers of Fundamental Physics 14 - FFP14, Jul 2014, Marseille, France
Lemaitre's Big Bang
Frontiers of Fundamental Physics (FFP14), Jul 2014, Marseille, France. pp.214
Fusion procedure for cyclotomic Hecke algebras
Symmetry, Integrability and Geometry : Methods and Applications, 2014, pp.13
Chiral fermions as classical massless spinning particles
2014
Idempotents for Birman–Murakami–Wenzl algebras and reflection equation
Advances in Theoretical and Mathematical Physics, 2014, pp.25
Fusion procedure for Coxeter groups of type B and complex reflections groups G(m,1,n)
Proceedings of the American Mathematical Society, 2014, pp.13
