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 |
Cyclotomic shuffles
12th International Workshop on Supersymmetries and Quantum Symmetries, Jul 2017, Dubna, Russia. pp.867-872, (10.1134/S1063779618050325)
Carroll symmetry of plane gravitational waves
Classical and Quantum Gravity, 2017, 34 (17), pp.175003. (10.1088/1361-6382/aa7f62)
The memory effect for plane gravitational waves
Modern Physics Letters B, 2017, 772, pp.743 - 746. (10.1016/j.physletb.2017.07.050)
Shuffle analogues for complex reflection groups G(m, 1, n)
Mathematical Physics [math-ph]. 2017
Heat trace for Laplace type operators with non-scalar symbols
Journal of Geometry and Physics, 2017, 116, pp.90-118. (10.1016/j.geomphys.2017.01.014)
Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
Classical and Quantum Gravity, 2017, 34 (8), pp.085004. (10.1088/1361-6382/aa627d)
Conformal and projective symmetries in Newtonian cosmology
Journal of Geometry and Physics, 2017, 112, pp.197--209. (10.1016/j.geomphys.2016.11.012)
The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries
International Review of Science, 2017, (10.48550/arXiv.1701.02930)
Soft gravitons and the memory effect for plane gravitational waves
Physical Review D, 2017, 96 (6), pp.064013. (10.1103/PhysRevD.96.064013)
Conjugation Properties of Tensor Product and Fusion Coefficients
Letters in Mathematical Physics, 2017, 107 (2), pp.291-299. (10.1007/s11005-016-0901-3)
