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 |
Diagrammes de Young et élément de battage de l'algèbre de Hecke
Physique mathématique [math-ph]. 2013
Drinfeld doubles for finite subgroups of SU(2) and SU(3) Lie groups
Symmetry, Integrability and Geometry : Methods and Applications, 2013, 9 (039), http://www.emis.de/journals/SIGMA/2013/039/. (10.3842/SIGMA.2013.039)
On representations of complex reflection groups G(m,1,n)
Theoretical and Mathematical Physics, 2013, 174 (1), pp.95-108. (10.1007/s11232-013-0008-2)
On a class of integrable systems with a quartic first integral
Regular and Chaotic Dynamics, 2013, 18 (04), pp.394-424. (10.1134/S1560354713040060)
Transverse Shifts in Paraxial Spinoptics
Journal of Optics, 2013, 15 (014005), 4pp. (10.1088/2040-8978/15/1/014005)
Formulation of gauge theories on transitive Lie algebroids
Journal of Geometry and Physics, 2013, 64, pp.174. (10.1016/j.geomphys.2012.11.005)
Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach
Advances in Applied Mathematics, 2013, 51 (03), pp.345-358. (10.1016/j.aam.2013.04.006)
Spectral action beyond the weak-field approximation
Communications in Mathematical Physics, 2012, 316 (3), pp.595-613. (10.1007/s00220-012-1587-8)
Quantization via Deformation of Prequantization
Reports on Mathematical Physics, 2012, 70 (03), pp.361-374. (10.1016/S0034-4877(12)60051-2)
On a weak Gauss law in general relativity and torsion
Classical and Quantum Gravity, 2012, 29 (24), pp.245009. (10.1088/0264-9381/29/24/245009)
