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

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

109 results
Journal article
Christian Duval, Serge Lazzarini
Schrödinger Manifolds
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2012, 45, pp.395203. 〈10.1088/1751-8113/45/39/395203〉
Direction of work or proceedings
Joseph Kouneiher, Cécile Barbachoux, Thierry Masson, Dimitri Vey
Proceedings, 11th Annual International Symposium on Frontiers of fundamental physics (FFP11) : Paris, France, July 6-9, 2010
Kouneiher, Joseph; Barbachoux, Cécile; Masson, Thierry; Vey, Dimitry. 11th Annual International Symposium on Frontiers of fundamental physics (FFP11), Jul 2010, Paris, France. 1446, 2012, 978-0-7354-1043-5. 〈10.1063/1.4727985〉. 〈http://scitation.aip.org〉
Conference paper
Robert Coquereaux
Character tables (modular data) for Drinfeld doubles of finite groups
7th International Conference on Mathematical Methods in Physics, Apr 2012, Rio de Janeiro, Brazil. http://pos.sissa.it/archive/conferences/175/024/ICMP%202012_024.pdf, pp.PoS(ICMP 2012)024, 2012
Journal article
Serge Lazzarini, Thierry Masson
Connections on Lie algebroids and on derivation-based noncommutative geometry
Journal of Geometry and Physics, Elsevier, 2012, 62, pp.387-402. 〈10.1016/j.geomphys.2011.11.002〉
Book Section
Thierry Masson
Gauge theories in noncommutative geometry
Joseph Kouneiher Cécile Barbachoux Thierry Masson and Dimitry Vey. Frontiers of Fundamental Physics: The Eleventh International Symposium, AIP, pp.73, 2012, AIP Conference Proceedings
Journal article
B. Iochum, T. Masson, A. Sitarz
$\kappa$-deformation, affine group and spectral triples
Banach Center Publications, Institute of Mathematics Polish Academy of Sciences, 2012, 98, pp.261--291. 〈10.4064/bc98-0-11〉
Preprint, Working paper
Cédric Fournel, Serge Lazzarini, Thierry Masson
Local description of generalized forms on transitive Lie algebroids and applications
Journal article
Christian Duval, Peter Horvathy
Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2011, 44, 335203 (21pp). 〈10.1088/1751-8113/44/33/335203〉
Journal article
Christian Duval, Galliano Valent
A new integrable system on the sphere and conformally equivariant quantization
Journal of Geometry and Physics, Elsevier, 2011, 61 (1), pp.1329-1347. 〈10.1016/j.geomphys.2011.02.020〉
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
109 results