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Geometry, Physics, and Symmetries

Group “Fundamental Interactions”

Our activities are centered on the mathematical description of physical laws, in particular laws that govern fundamental interactions. The necessary tools are often of geometric, algebraic, combinatorial, analytic or functional nature. Some results or problems lead to the emergence of new mathematical structures needing a dedicated study. Others have direct physical applications.

Fundamental laws of nature, at the classical level, are naturally expressed in terms of geometry (for instance the notion of connection on a bundle appears in our understanding of both gravity and strong or electroweak interactions), and symmetries of the physical world are usually described, classically, by group theoretical constructions, in particular representation theory. Geometry finds its roots in the study of symmetries but one knows that mechanics itself uses geometry, in particular symplectic geometry, for its own formulation. A quantum description of physics requires not only the above tools but also appropriate generalizations of these notions. Approaches leading to theories of quantum gravity using non-commutative geometry, for instance, need mathematical descriptions where space-time (actually its algebra of functions) is replaced by a non-commutative algebra; moreover many developments of quantum field theory use generalizations of the notion of group, for instance supersymmetric theories use Lie super-algebras, and conformal field theory or string theory, as well as the theory of integrable systems, use concepts coming from affine Lie algebras and quantum groups.
Our activities focus around the above themes.

Directory of Members

BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Iochum Bruno Emeritus
+33.4.91.26.97.96 Email
Krajewski Thomas University faculty
+33.4.91.26.95.61 Email
Lazzarini Serge University faculty
Chef de l’équipe « Géométrie, Physique et Symétries »
Web editor
Correspondant FRUMAM
+33.4.91.26.97.94 Email
Luminet Jean-Pierre Guest
+33.4.91.26.95.19 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
+33.4.91.26.97.96 Email
Ogievetsky Oleg University faculty
+33.4.91.26.95.33 Email
Schücker Thomas University faculty
Chef du Groupe « Interactions fondamentales »
+33.4.91.26.95.61 Email
Triay Roland University faculty
+33.4.91.26.95.19 Email

List of Publications

110 results
Journal article
Bruno Iochum, Thierry Masson, Thomas Schücker, Andrzej Sitarz
Compact $\kappa$-deformation and spectral triples
Reports on Mathematical Physics, Elsevier, 2011, 68 (1), pp.37-64
Journal article
Bruno Iochum, Thierry Masson, Thomas Schucker, Andrzej Sitarz
$\kappa$-Deformation and Spectral Triples
Acta Physica Polonica B, Jagellonian University, Cracow, 2011, 4 (3), pp.305. 〈10.5506/APhysPolBSupp.4.305〉
Preprint, Working paper
Thomas Schucker
Lensing in the Einstein-Straus solution
2011
Preprint, Working paper
Thomas Schucker
The noncommutative standard model, post- and predictions
2010
Preprint, Working paper
Thierry Masson, Jean-Christophe Wallet
A Remark on the Spontaneous Symmetry Breaking Mechanism in the Standard Model
2010
Journal article
Robert Coquereaux
Global dimensions for Lie groups at level k and their conformally exceptional quantum subgroups
Revista de la Union Matematica Argentina, 2010, 51 (2), pp.17-42
Journal article
R. Coquereaux, R. Rais, E. H. Tahri
Exceptional quantum subgroups for the rank two Lie algebras B2 and G2
Journal of Mathematical Physics, American Institute of Physics (AIP), 2010, 51 (9), pp.092302. 〈10.1063/1.3476319〉
Journal article
Christian Duval
Schwarzian derivative and Numata Finsler structures
Advances in Pure and Applied Mathematics, De Gruyter, 2010, 1, pp.1
Journal article
R. Coquereaux, E. Isasi, G. Schieber
Notes on TQFT wire models and coherence equations for SU(3) triangular cells
Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2010, 6, pp.099. 〈10.3842/SIGMA.2010.099〉
Journal article
Christian Duval, Péter A. Horvathy
Non-relativistic conformal symmetries and Newton-Cartan structures
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42, pp.465206
110 results

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