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 |
The Dressing Field Method of Gauge Symmetry Reduction: Presentation and Examples
Geometric Methods in Physics XXXVI: Workshop and Summer School, Białowieża, Poland, 2017, pp.199-205, 2019, Trends in Mathematics, 9783030011567. (10.1007/978-3-030-01156-7_21)
Gravitational Music. On My Collaboration with Hèctor Parra
Contemporary Music Review, 2019, 38 (1-2), pp.193-205. (10.1080/07494467.2019.1578129)
A classification of global conformal invariants
Journal of Physics A: Mathematical and Theoretical, 2019, 52 (11), pp.115201. (10.1088/1751-8121/ab01af)
Critical configurations of solid bodies and the Morse theory of MIN functions
Russian Mathematical Surveys, 2019, 74 (4), pp.631-657. (10.4213/rm9899)
Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model
Physical Review D, 2019, 99 (12), pp.126014. (10.1103/PhysRevD.99.126014)
Program computing the asymptotic expansion coefficients of the heat-trace for a nonminimal Laplace type operator
2019, (swh:1:dir:584ba08ee05ade4c3408de5b6056ac7eec0412b3;origin=https://hal.archives-ouvertes.fr/hal-03599607;visit=swh:1:snp:e6d920e4c9ad4ab0900baeb34421aaf8d77e29fb;anchor=swh:1:rel:9d0979a4b0f246988b0582ec028f94a5a58b0a9f;path=/)
How does the photon’s spin affect gravitational wave measurements?
Physical Review D, 2019, 100 (6), pp.064050. (10.1103/PhysRevD.100.064050)
The Horn Problem for Real Symmetric and Quaternionic Self-Dual Matrices
Symmetry, Integrability and Geometry : Methods and Applications, 2019, 15, pp.029. (10.3842/SIGMA.2019.029)
Gravitational birefringence of light in Schwarzschild spacetime
Physical Review D, 2019, 99 (12), pp.124037. (10.1103/PhysRevD.99.124037)
A Tutte Polynomial for Maps
Combinatorics, Probability and Computing, 2018, 27 (06), pp.913-945. (10.1017/S0963548318000081)
