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 |
Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and $AF$ algebras
Journal of Geometry and Physics, 2023, 187, pp.104784. (10.1016/j.geomphys.2023.104784)
On balanced and abelian properties of circular words over a ternary alphabet
Theoretical Computer Science, 2023, 939, pp.227-236. (10.1016/j.tcs.2022.10.027)
Double scaling limit of the prismatic tensor model
Journal of Physics A: Mathematical and Theoretical, 2023, 56 (23), pp.235401. (10.1088/1751-8121/accf4e)
About integer-valued variants of the theta and $6j$ symbols
Journal of Mathematical Physics, 2023, 64 (3), pp.031703. (10.1063/5.0131150)
Noncommutative Geometry and Gauge theories on AF algebras
Physics [physics]. centre de physique théorique marseille, 2022. English. (NNT : )
The Art of Unlocking
The Mathematical Intelligencer, 2022, 44 (4), pp.320-325. (10.1007/s00283-022-10210-0)
Axial Bianchi IX and its Lemaître-Hubble diagram
2022
Planar Carrollean dynamics, and the Carroll quantum equation
Journal of Geometry and Physics, 2022, 179, pp.104574. (10.1016/j.geomphys.2022.104574)
Anyonic spin-Hall effect on the black hole horizon
Physical Review D, 2022, 106 (12), pp.L121503. (10.1103/PhysRevD.106.L121503)
Extremal Cylinder Configurations II: Configuration O6
Experimental Mathematics, 2022, 31 (2), pp.486-496. (10.1080/10586458.2019.1641768)
