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 |
La physique du XIXe siècle face au concept de paradigme
L'épistémologique et interdisciplinarité, A paraître
Constructive matrix theory for higher order interaction II: Hermitian and real symmetric cases
Annales Henri Poincaré, 2022, 23 (10), pp.3431-3452. (10.1007/s00023-022-01170-4)
SU(3) higher roots and their lattices
Patrick Flandrin, Stéphane Jaffard, Thierry Paul, Bruno Torresani. Theoretical Physics, Wavelets, Analysis, Genomics : An Indisciplinary Tribute to Alex Grossmann, Springer, In press, Theoretical Physics, Wavelets, Analysis, Genomics An Indisciplinary Tribute to Alex Grossmann, ISBN-10 3030458466 ISBN-13 978-3030458461 ISSN 2296-5009
Fully extended BV-BFV description of General Relativity in three dimensions
Advances in Theoretical and Mathematical Physics, 2022, 26 (3), pp.595-642. (10.4310/ATMP.2022.v26.n3.a2)
Derivation-based Noncommutative Field Theories on $AF$ algebras
International Journal of Geometric Methods in Modern Physics, 2021, 18 (13), pp.2150213. (10.1142/S0219887821502133)
About left-invariant geometry and homogeneous pseudo-Riemannian Einstein structures on the Lie group SU(3)
2021
Cayley–Hamilton theorem for symplectic quantum matrix algebras
Journal of Geometry and Physics, 2021, 165, pp.104211. (10.1016/j.geomphys.2021.104211)
The Dark Matter Enigma
2021
The Six Cylinders Problem: $\mathbb{D}_{3}$-symmetry Approach
Discrete and Computational Geometry, 2021, 65 (2), pp.385-404. (10.1007/s00454-019-00064-3)
Extremal Cylinder Configurations I: Configuration $C_{\mathfrak{m}}$
Discrete and Computational Geometry, 2021, 66 (1), pp.140-164. (10.1007/s00454-020-00244-6)
