Centre de Physique Théorique

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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
Coquereaux Robert Emeritus
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Iochum Bruno Emeritus
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Krajewski Thomas University faculty
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Lazzarini Serge University faculty
Chef de l’équipe « Géométrie, Physique et Symétries »
Web editor
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Marsot Loïc PhD candidate
Masson Thierry Researcher
Communications manager
Correspondant valorisation
Correspondant LabEx Archimède
Correspondant FRUMAM
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Ogievetsky Oleg University faculty
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Schücker Thomas University faculty
Chef du Groupe « Interactions fondamentales »
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Triay Roland University faculty
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List of Publications

122 results
Journal article
Christian Duval, G. W. Gibbons, P. A. Horvathy
Conformal Carroll groups
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2014, 47 (33), pp.335204. ⟨10.1088/1751-8113/47/33/335204⟩
Preprint, Working paper
Christian Duval
Polarized Spinoptics and Symplectic Physics
Cédric Fournel
Théories de jauge et connexions généralisées sur les algébroïdes de Lie transitifs
Mathematical Physics [math-ph]. Aix-Marseille Université, 2013. English
Conference paper
Galliano Valent, Christian Duval, Vsevolod Shevchishin
Explicit metrics for a class of two-dimensional cubically superintegrable systems
Finite dimensional integrable systems: on the crossroad of algebra, geometry and physics, Jul 2013, Marseille, France. pp.354-372, ⟨10.1016/j.geomphys.2014.08.004⟩
Master thesis
Pierre Doyeux
Diagrammes de Young et élément de battage de l'algèbre de Hecke
Physique mathématique [math-ph]. 2013
Journal article
Robert Coquereaux, Jean-Bernard Zuber
Drinfeld doubles for finite subgroups of SU(2) and SU(3) Lie groups
Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2013, 9 (039), http://www.emis.de/journals/SIGMA/2013/039/. ⟨10.3842/SIGMA.2013.039⟩
Journal article
Gérard H. E. Duchamp, Nguyen Hoang-Nghia, Thomas Krajewski, Adrian Tanasa
Recipe theorem for the Tutte polynomial for matroids, renormalization group-like approach
Advances in Applied Mathematics, Elsevier, 2013, 51 (03), pp.345-358. ⟨10.1016/j.aam.2013.04.006⟩
Journal article
Cédric Fournel, Serge Lazzarini, Thierry Masson
Formulation of gauge theories on transitive Lie algebroids
Journal of Geometry and Physics, Elsevier, 2013, 64, pp.174. ⟨10.1016/j.geomphys.2012.11.005⟩
Journal article
Galliano Valent
On a class of integrable systems with a quartic first integral
Regular and Chaotic Dynamics, MAIK Nauka/Interperiodica, 2013, 18 (04), pp.394-424. ⟨10.1134/S1560354713040060⟩
Journal article
Christian Duval, P. A. Horvathy, P. M. Zhang
Transverse Shifts in Paraxial Spinoptics
Journal of Optics, Institute of Physics (IOP), 2013, 15 (014005), 4pp. ⟨10.1088/2040-8978/15/1/014005⟩
122 results