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 |
Conformal embeddings and quantum graphs with self-fusion
São Paulo Journal of Mathematical Sciences, 2009, 3 (1), pp.239-262
On the projective geometry of the supercircle: a unified construction of the super cross-ratio and Schwarzian derivative
International Mathematics Research Notices, 2008, 2008, pp.rnn054. (10.1093/imrn/rnn054)
Finsler Spinoptics
Communications in Mathematical Physics, 2008, 283, pp.701-727
From conformal embeddings to quantum symmetries: an exceptional SU(4) example
Journal of Physics: Conference Series, 2008, 103, pp.012006
Spectral action in noncommutative geometry: An example
Journal of Physics: Conference Series, 2008, 103, pp.012019. (10.1088/1742-6596/103/1/012019)
Geometrical Spinoptics and the Optical Hall Effect
Journal of Geometry and Physics, 2007, 57
Seesaw and noncommutative geometry
Physics Letters B, 2007, B654, pp.127-132
Quantum integrability of quadratic Killing tensors
Journal of Mathematical Physics, 2005, 46, pp.053516. (10.1063/1.1899986)
Equation of motion for N = 4 supergravity with antisymmetric tensor from its geometric description in central charge superspace
Journal of High Energy Physics, 2002, 2002 (02), pp.040-040. (10.1088/1126-6708/2002/02/040)
Singular and nonsingular eigenvectors for the Gaudin model
Journal of Mathematical Physics, 2001, 42 (8), pp.3497-3516. (10.1063/1.1379750)
