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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

Attard Jérémy PhD candidate
Bizi Nadir PhD candidate
BULGAKOVA Daria PhD candidate
Coquereaux Robert Researcher
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Duval Christian Emeritus
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Giovannetti Gabriel ATER
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
Correspondant FRUMAM
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Luminet Jean-Pierre Guest
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Marsot Loïc PhD candidate
Masson Thierry Researcher
Communications manager
Correspondant valorisation
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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

97 results
Journal article
Christian Duval, G. W. Gibbons, P. A. Horvathy, P. M. Zhang
Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time
Classical and Quantum Gravity, IOP Publishing, 2014, 31 (085016), 24pp. 〈10.1088/0264-9381/31/8/085016〉
Journal article
Christian Duval, G. W. Gibbons, P. A. Horvathy
Conformal Carroll groups and BMS symmetry
Classical and Quantum Gravity, IOP Publishing, 2014, 31 (092001), 8pp. 〈10.1088/0264-9381/31/9/092001〉
Journal article
Cédric Fournel, Jordan François, Serge Lazzarini, Thierry Masson
Gauge invariant composite fields out of connections, with examples
International Journal of Geometric Methods in Modern Physics, World Scientific Publishing, 2014, pp.1450016. 〈10.1142/S0219887814500169〉
Book Section
François Jordan, Lazzarini Serge, Masson Thierry
Gauge field theories: various mathematical approaches
Eckstein, Michal; Heller, Michael; Szybka, Sebastian J. Mathematical Structures of the Universe, Copernicus Center Press, 2014, 978-83-7886-107-2
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〉
Direction of work or proceedings
Eric Kajfasz, Thierry Masson, Roland Triay
Proceedings, 14th International Symposium Frontiers of Fundamental Physics (FFP14): Marseille, France, July 15-18, 2014
Kajfasz, Eric; Masson, Thierry; Triay, Roland. Frontiers of Fundamental Physics 14, Jul 2014, Marseille, France. PoS, 2014, 〈http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=224〉
Journal article
Robert Coquereaux, Jean-Bernard Zuber
Conjugation properties of tensor product multiplicities
Journal of Physics A General Physics, Institute of Physics (IOP), 2014, 47, pp.455202. 〈10.1088/1751-8113/47/45/455202〉
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. Journal of Geometry and Physics, 87, pp.354-372, 2015, 〈http://www.cpt.univ-mrs.fr/fdis13/〉. 〈10.1016/j.geomphys.2014.08.004〉
97 results