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
Basile Herlemont, Oleg Ogievetsky
Differential Calculus on h-Deformed Spaces
Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2017, Special Issue on Recent Advances in Quantum Integrable Systems, 13 (13), pp.082. 〈10.3842/SIGMA.2017.082〉
Journal article
S. Khoroshkin, O. Ogievetsky
Diagonal reduction algebra and the reflection equation
Israël Journal of Mathematics, The Hebrew University Magnes Press, 2017, 221 (1), pp.705-729. 〈10.1007/s11856-017-1571-2〉
Journal article
Christian Duval, G. W. Gibbons, P. A. Horvathy, P. -M. Zhang
Carroll symmetry of plane gravitational waves
Classical and Quantum Gravity, IOP Publishing, 2017, 34 (17), pp.175003. 〈http://stacks.iop.org/0264-9381/34/i=17/a=175003〉
Journal article
P.-M. Zhang, C. Duval, G.W. Gibbons, P.A. Horvathy
The memory effect for plane gravitational waves
Modern Physics Letters B, World Scientific Publishing, 2017, 772, pp.743 - 746. 〈10.1016/j.physletb.2017.07.050〉
Master thesis
Varvara Petrova
Shuffle analogues for complex reflection groups G(m, 1, n)
Mathematical Physics [math-ph]. 2017
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, J. François
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〉
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
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
Jean-Pierre Luminet
The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries
International Review of Science, 2017
109 results