Centre de Physique Théorique

Home > Research teams > Geometry, Physics, and Symmetries

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

Attard Jérémy PhD candidate
Email
Bizi Nadir PhD candidate
Email
BULGAKOVA Daria PhD candidate
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 Email
Duval Christian Emeritus
+33.4.91.26.97.97 Email
Giovannetti Gabriel ATER
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
+33.4.91.26.97.94 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

97 results
Journal article
Bruno Iochum, Thierry Masson
Heat trace for Laplace type operators with non-scalar symbols
Journal of Geometry and Physics, Elsevier, 2017, 116, pp.90-118. 〈10.1016/j.geomphys.2017.01.014〉
Journal article
François Jordan, Jérémy Attard
Tractors and twistors from conformal Cartan geometry: a gauge theoretic approach II. Twistors
Classical and Quantum Gravity, IOP Publishing, 2017, 34 (8), pp.085004. 〈10.1088/1361-6382/aa627d〉
Preprint, Working paper
J. Attard, J. François, S. Lazzarini, T. Masson
The dressing field method of gauge symmetry reduction, a review with examples
2017
Journal article
C. Duval, G.W. Gibbons, P.A. Horváthy
Conformal and projective symmetries in Newtonian cosmology
Journal of Geometry and Physics, Elsevier, 2017, 112, pp.197--209. 〈10.1016/j.geomphys.2016.11.012〉
Journal article
Thomas Krajewski
A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries
Advances in High Energy Physics, Hindawi Publishing Corporation, 2017, 2017, pp.4098720. 〈10.1155/2017/4098720〉
Journal article
Kevin Falk
Examples of infinite direct sums of spectral triples
Journal of Geometry and Physics, Elsevier, 2017, 112, pp.240 - 251. 〈10.1016/j.geomphys.2016.10.019〉
Journal article
B Herlemont, O Ogievetsky
Rings of h-deformed differential operators
Theoretical and Mathematical Physics, 2017, 192 (2), pp.1218-1229. 〈10.1134/S0040577917080104〉
Journal article
Robert Coquereaux, Jean-Bernard Zuber
Conjugation Properties of Tensor Product and Fusion Coefficients
Letters in Mathematical Physics, Springer Verlag, 2017, 107 (2), pp.291-299. 〈10.1007/s11005-016-0901-3〉
Journal article
M. Cariglia, Christian Duval, G.W. Gibbons, P.A. Horváthy
Eisenhart lifts and symmetries of time-dependent systems
Annals of Physics, 2016, 373, pp.631--654. 〈http://www.journals.elsevier.com/annals-of-physics〉. 〈10.1016/j.aop.2016.07.033〉
Journal article
M Elbistan, Christian Duval, Peter A. Horvathy, P. -M. Zhang
Duality and helicity: a symplectic viewpoint
Physics Letters B, Elsevier, 2016, 761, pp.265-268. 〈10.1016/j.physletb.2016.08.041〉
97 results

Calendar