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 |
Alternating subalgebras of Hecke algebras and alternating subgroups of braid groups
Communications in Algebra, 2014, pp.16
Rings of fractions of reduction algebras
Algebras and Representation Theory, 2014, pp.DOI: 10.1007/s10468-012-9397-4
Quantum McKay correspondence and global dimensions for fusion and module-categories associated with Lie groups
Journal of Algebra, 2014, 398, pp.Pages 258-283. (10.1016/j.jalgebra.2013.09.030)
Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
Classical and Quantum Gravity, 2014, 31 (085016), 24pp. (10.1088/0264-9381/31/8/085016)
Bianchi I meets the Hubble diagram
Monthly Notices of the Royal Astronomical Society, 2014, 444 (3), pp.2820-2836. (10.1093/mnras/stu1656)
Evry Leon Schatzman
Biographical Encyclopedia of Astronomers, 2014
Gauge invariant composite fields out of connections, with examples
International Journal of Geometric Methods in Modern Physics, 2014, pp.1450016. (10.1142/S0219887814500169)
Conformal Carroll groups and BMS symmetry
Classical and Quantum Gravity, 2014, 31 (092001), 8pp. (10.1088/0264-9381/31/9/092001)
Heat trace and spectral action on the standard Podles sphere
Communications in Mathematical Physics, 2014, 332 (2), pp.627-668. (10.1007/s00220-014-2054-5)
Spectral Geometry
A. Cardonna, C. Neira-Jemenez, H. Ocampo, S. Paycha and A. Reyes-Lega. Spectral Geometry, Aug 2011, Villa de Leyva, Colombia. World Scientific, 2014, Geometric, Algebraic and Topological Methods for Quantum Field Theory, 978-981-4460-04-0
