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 |
$\kappa$-deformation, affine group and spectral triples
Banach Center Publications, 2012, 98, pp.261--291. (10.4064/bc98-0-11)
Gauge theories in noncommutative geometry
Joseph Kouneiher Cécile Barbachoux Thierry Masson and Dimitry Vey. Frontiers of Fundamental Physics: The Eleventh International Symposium, AIP, pp.73, 2012, AIP Conference Proceedings
A new fusion procedure for the Brauer algebra and evaluation homomorphisms
International Mathematics Research Notices, 2012, 2012 (11), pp.2571-2606. (10.1093/imrn/rnr126)
Cyclotomic Hecke algebras: Jucys-Murphy elements, representations, classical limit
2011
Local description of generalized forms on transitive Lie algebroids and applications
2011
Dynamics of voids and their shapes in redshift space
Journal of Cosmology and Astroparticle Physics, 2011, 08, pp.026. (10.1088/1475-7516/2011/08/026)
Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
Journal of Physics A: Mathematical and Theoretical, 2011, 44, 335203 (21pp). (10.1088/1751-8113/44/33/335203)
Structure constants of diagonal reduction algebras of gl type
Symmetry, Integrability and Geometry : Methods and Applications, 2011, 7, pp.064. (10.3842/SIGMA.2011.064)
On sums of tensor and fusion multiplicities
Journal of Physics A: Mathematical and Theoretical, 2011, 44, pp.295208
A new integrable system on the sphere and conformally equivariant quantization
Journal of Geometry and Physics, 2011, 61 (1), pp.1329-1347. (10.1016/j.geomphys.2011.02.020)
