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 |
Notes on TQFT wire models and coherence equations for SU(3) triangular cells
Symmetry, Integrability and Geometry : Methods and Applications, 2010, 6, pp.099. (10.3842/SIGMA.2010.099)
Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
Journal of Mathematical Physics, 2010, 51 (9), pp.092302. (10.1063/1.3476319)
Schwarzian derivative and Numata Finsler structures
Advances in Pure and Applied Mathematics, 2010, 1, pp.1
Diagonal reduction algebras of gl type
Functional Analysis and Its Applications, 2010, 44 (3), pp.182-198. (10.1007/s10688-010-0023-0)
$\Lambda$ effect in the cosmological expansion of voids
Journal of Cosmology and Astroparticle Physics, 2010, 2010 (11), pp.022 (10.1088/1475-7516/2010/11/022)
Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups
Revista de la Unión Matemática Argentina, 2010, 51 (2), pp.17-42
Nombres de Bernoulli et une formule de Schlömilch-Ramanujan
Moscow Mathematical Journal, 2010, 10 (4), pp.765--788, 839
BRST charges for finite nonlinear algebras
Physics of Particles and Nuclei Letters [PisВ'ma v Zhurnal Fizika Elementarnykh Chastits i Atomnogo Yadra / Pisʹma v žurnal "Fizika èlementarnyh častic i atomnogo âdra"], 2010, 7 (4), pp.223-228. (10.1134/S1547477110040011)
Non-relativistic conformal symmetries and Newton-Cartan structures
Journal of Physics A: Mathematical and Theoretical, 2009, 42, pp.465206
Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings
Symmetry, Integrability and Geometry : Methods and Applications, 2009, 5 (044), http://www.emis.de/journals/SIGMA/2009/044/. (10.3842/SIGMA.2009.044)
