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 |
A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries
Advances in High Energy Physics, 2017, 2017, pp.4098720. (10.1155/2017/4098720)
Gravitational birefringence of light in Robertson-Walker cosmologies
Physical Review D, 2017, 96 (4), pp.043517. (10.1103/PhysRevD.96.043517)
Rings of h-deformed differential operators
Theoretical and Mathematical Physics, 2017, 192 (2), pp.1218-1229. (10.1134/S0040577917080104)
Examples of infinite direct sums of spectral triples
Journal of Geometry and Physics, 2017, 112, pp.240 - 251. (10.1016/j.geomphys.2016.10.019)
Wigner law for matrices with dependent entries—a perturbative approach
Journal of Physics A: Mathematical and Theoretical, 2017, 50 (16), pp.16LT02. (10.1088/1751-8121/aa64ae)
Mathematical Foundations of Quantum Field Theory : A volume dedicated to the Memory of Raymond Stora
Elsevier. , 912, pp.1-484, 2016, Nuclear Physics B
Duality and helicity: a symplectic viewpoint
Physics Letters B, 2016, 761, pp.265-268. (10.1016/j.physletb.2016.08.041)
A Note on Weyl invariance in gravity and the Wess-Zumino functional
Nuclear Physics B, 2016, Mathematical Foundations of Quantum Field Theory: A volume dedicated to the Memory of Raymond Stora, 912, pp.289-304. (10.1016/j.nuclphysb.2016.07.016)
Jean-Pierre Luminet - La forme de l'espace, des trous noirs au multivers
2016
On some properties of SU(3) fusion coefficients
Nuclear Physics B, 2016, Mathematical Foundations of Quantum Field Theory: A volume dedicated to the Memory of Raymond Stora., 912, pp.119-150. (10.1016/j.nuclphysb.2016.05.029)
