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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 Emeritus
+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
+33.4.91.26.97.94 Email
Marsot Loïc PhD candidate
Email
Masson Thierry Researcher
Communications manager
Correspondant valorisation
Correspondant LabEx Archimède
Correspondant FRUMAM
+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

122 results
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
Jean-Pierre Luminet
The Reception of the Copernican Revolution Among Provençal Humanists of the Sixteenth and Seventeenth Centuries
International Review of Science, 2017
Journal article
Robert Coquereaux, Jean-Bernard Zuber
Conjugation Properties of Tensor Product and Fusion Coefficients
Letters in Mathematical Physics, Springer Verlag, 2017, 107 (2), pp.291-299. ⟨10.1007/s11005-016-0901-3⟩
Journal article
B Herlemont, O Ogievetsky
Rings of h-deformed differential operators
Theoretical and Mathematical Physics, Consultants bureau, 2017, 192 (2), pp.1218-1229. ⟨10.1134/S0040577917080104⟩
Journal article
C. Duval, T. Schücker
Gravitational birefringence of light in Robertson-Walker cosmologies
Physical Review D, American Physical Society, 2017, 96 (4), pp.043517. ⟨10.1103/PhysRevD.96.043517⟩
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
Thomas Krajewski
A Renormalisation Group Approach to the Universality of Wigner’s Semicircle Law for Random Matrices with Dependent Entries
Advances in High Energy Physics, Hindawi Publishing Corporation, 2017, 2017, pp.4098720. ⟨10.1155/2017/4098720⟩
122 results

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