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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
Email
Coquereaux Robert Researcher
+33.4.91.26.95.18 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
+33.4.91.26.97.96 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

109 results
Journal article
M. Elbistan, Christian Duval, P. A. Horvathy, P. -M. Zhang
Helicity of spin-extended chiral particles
Physics Letters A, Elsevier, 2016, 380 (20), pp.1677-1683. 〈10.1016/j.physleta.2016.03.016〉
Other publication
Jean-Pierre Luminet
The Holographic Universe
Critical essay in : Inference: The International Review of Science, vol. 2, issue 1. 2016
Journal article
Bruno Iochum, Thierry Masson
Crossed product extensions of spectral triples
Journal of Noncommutative Geometry, European Mathematical Society, 2016, 10 (1), pp.65-133. 〈10.4171/JNCG/229〉
Thesis
Kevin Falk
Quantification de Berezin--Toeplitz et géométrie non commutative
Mathematical Physics [math-ph]. Centre de Physique Théorique, 2015. English
Journal article
Christian Duval, Serge Lazzarini
On the Schrödinger-Newton equation and its symmetries: a geometric view
Classical and Quantum Gravity, IOP Publishing, 2015, 32, pp.175006
Journal article
Christian Duval, M Elbistan, P.A. Horváthy, P.-M Zhang
Wigner–Souriau translations and Lorentz symmetry of chiral fermions
Physics Letters B, Elsevier, 2015, 742, pp.322-326. 〈10.1016/j.physletb.2015.01.048〉
Journal article
François Jordan, Lazzarini Serge, Thierry Masson
Nucleon spin decomposition and differential geometry
Physical Review D, American Physical Society, 2015, pp.045014. 〈10.1103/PhysRevD.91.045014〉
Journal article
Robert Coquereaux
The history of the universe is an elliptic curve
Classical and Quantum Gravity, IOP Publishing, 2015, 32 (11), pp.115013
Journal article
O. Ogievetsky, L. Poulain d'Andecy
Induced representations and traces for chains of affine and cyclotomic Hecke algebras
Journal of Geometry and Physics, Elsevier, 2015, 87, pp.354-372. 〈10.1016/j.geomphys.2014.07.005〉
Journal article
François Jordan, Serge Lazzarini, Thierry Masson
Residual Weyl symmetry out of conformal geometry and its BRST structure
Journal of High Energy Physics, Springer Verlag (Germany), 2015, 09, pp.195. 〈10.1007/JHEP09(2015)195〉
109 results

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