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 |
From orbital measures to Littlewood-Richardson coefficients and hive polytopes
Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2018, Combinatorics, Physics and their Interactions, 5 (3), pp.339-386. (10.4171/AIHPD/57)
Memory Effect for Impulsive Gravitational Waves
Class.Quant.Grav., 2018, 35 (6), pp.065011. (10.1088/1361-6382/aaa987)
Seeing Black Holes : from the Computer to the Telescope
Universe, 2018, 4 (8), pp.86. (10.3390/universe4080086)
Spectral Action in Noncommutative Geometry
Springer International Publishing, 27, 2018, SpringerBriefs in Mathematical Physics, (10.1007/978-3-319-94788-4)
Tractors and Twistors from conformal Cartan geometry: a gauge theoretic approach I. Tractors
Adv.Theor.Math.Phys., 2018, 22, pp.1831-1883. (10.4310/ATMP.2018.v22.n8.a1)
The dressing field method of gauge symmetry reduction, a review with examples
Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, Springer, pp.377-415, 2018, 978-3-319-64812-5. (10.1007/978-3-319-64813-2)
Determination of the cosmological parameters in the framework of the Friedmann-Lemaître model
Physics [physics]. Aix-Marseille Université, Faculté des Sciences – Luminy, Centre de Physique Théorique - UMR 7332, 2017. English. (NNT : )
Differential calculus on h-deformed spaces
Quantum Algebra [math.QA]. Aix-Marseille Université, 2017. English. (NNT : )
Differential Calculus on h-Deformed Spaces
Symmetry, Integrability and Geometry : Methods and Applications, 2017, Special Issue on Recent Advances in Quantum Integrable Systems, 2017 (13), pp.082. (10.3842/SIGMA.2017.082)
Diagonal reduction algebra and the reflection equation
Israel Journal of Mathematics, 2017, 221 (1), pp.705-729. (10.1007/s11856-017-1571-2)
