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 |
Global and local aspects of spectral actions
Journal of Physics A: Mathematical and Theoretical, 2012, 45 (37), pp.374020. (10.1088/1751-8113/45/37/374020)
Higgs-mass predictions
Acta Physica Polonica B, 2012, 43 (9), pp.1863. (10.5506/APhysPolB.43.1863)
Schrödinger Manifolds
Journal of Physics A: Mathematical and Theoretical, 2012, 45, pp.395203. (10.1088/1751-8113/45/39/395203)
Proceedings, 11th Annual International Symposium on Frontiers of fundamental physics (FFP11) : Paris, France, July 6-9, 2010
Kouneiher, Joseph; Barbachoux, Cécile; Masson, Thierry; Vey, Dimitry. 11th Annual International Symposium on Frontiers of fundamental physics (FFP11), Jul 2010, Paris, France. 1446, , 2012, 978-0-7354-1043-5. (10.1063/1.4727985)
Character tables (modular data) for Drinfeld doubles of finite groups
7th International Conference on Mathematical Methods in Physics, Apr 2012, Rio de Janeiro, Brazil. pp.PoS(ICMP 2012)024
Noncommutative ε-graded connections
Journal of Noncommutative Geometry, 2012, 6 (2), pp.343-387. (10.4171/JNCG/94)
Braidings of Tensor Spaces
Letters in Mathematical Physics, 2012, 100 (1), pp.17-28. (10.1007/s11005-011-0533-6)
Spectral action for torsion with and without boundaries
Communications in Mathematical Physics, 2012, 310 (2), pp.367-382. (10.1007/s00220-011-1406-7)
Half-quantum linear algebra
XXIX International Colloquium on Group-Theoretical Methods in Physics, 2012, Tianjin, China
Connections on Lie algebroids and on derivation-based noncommutative geometry
Journal of Geometry and Physics, 2012, 62, pp.387-402. (10.1016/j.geomphys.2011.11.002)
