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 |
Drinfeld-Jimbo quantum Lie algebra
Scientific and Human Legacy of Julius Wess, 2011, Donji Milanovac, Serbia. pp.149-157, (10.1142/S2010194512006812)
Spectral triples and manifolds with boundary
Journal of Functional Analysis, 2011, 260 (1), pp.117-134. (10.1016/j.jfa.2010.09.006)
$\kappa$-Deformation and Spectral Triples
Acta Physica Polonica B, 2011, 4 (3), pp.305. (10.5506/APhysPolBSupp.4.305)
Jucys-Murphy elements for Birman-Murakami-Wenzl 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"], 2011
Compact $\kappa$-deformation and spectral triples
Reports on Mathematical Physics, 2011, 68 (1), pp.37-64. (10.1016/S0034-4877(11)60026-8)
Tadpoles and commutative spectral triples
Journal of Noncommutative Geometry, 2011, 5 (3), pp.299-329. (10.4171/JNCG/77)
R-matrices in Rime
Advances in Theoretical and Mathematical Physics, 2010, 14 (02), pp.439-505
Lensing in the Einstein-Straus solution
2010
The noncommutative standard model, post- and predictions
2010
A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model
2010
