Research themes


Research in the FYMA group is devoted to problems in mathematical physics, statistical physics and theoretical physics of fundamental interactions. In addition, there is a substantial activity in history of science.

Development and applications of various algebraic and group-theoretical techniques (J.-P. Antoine)

• Generalized coherent states: A theory of generalized coherent states has been developed in the last few years, starting from the notion of a group representation square integrable modulo a subgroup. Various extensions are now under study : discretization, the case of discrete groups (e.g., crystallographic groups) and of semigroups, application to quantization, link with Wigner functions. Several applications are planned, for instance, in quantum optics and in atomic physics.
• Wavelet analysis: In the case of the affine groups, the previous theory yields the continuous wavelet transform. The study focuses on the discretization of the latter and its application to various types of signals, both one-dimensional (NMR spectra, climatological or geophysical time series, signals with gaps) and two-dimensional (image processing, e.g.. in medical imagery, in astrophysics, in quasicrystallography, in the detection of symmetries in pattern). Particular emphasis is given to the design of fast algorithms.
• Partial operator algebras: A general theory of partial operator algebras has been setup in the last few years. Various extensions related to physical applications are being considered presently (representations, normal states, standard generalized vectors, weights, modular theory of Tomita-Takesaki, dynamical systems, ...).

Renormalization group and nonlinear differential equations (J. Bricmont)

• KAM Theory: Application of renormalization group ideas to prove the convergence of resummed perturbation series in classical mechanics (KAM and Eliasson theory).
• Stochastic nonlinear equations: Study of the ergodic properties of the two-dimensional Navier-Stokes equations with random forcing.

Two-dimensional conformal field theory (Ph. Ruelle)

• Conformal field theory : Relations between critical phenomena and their description in terms of conformal field theories. In two dimensions, this correspondence is particularly powerful due to the infinite dimensionality of the conformal algebra. The specific problems we currently address in the two-dimensional context concern the properties of conformal field theories when they are formulated in various geometries (plane, torus, cylinder). Questions which are connected to these properties include the classification of conformal field theories, the investigation of their symmetries, and the study of conformally invariant boundary conditions in the case of surfaces with boundaries. All these problems have rather puzzling connections with seemingly unrelated mathematical areas, which are under investigation too.
• Dynamical systems: Study of certain dynamical processes, defined in terms of discrete cellular automata, which exhibit critical properties, similar to the those observed in equilibrium statistical models. More specifically, the sandpile model -a canonical example, as is the Ising model in equilibrium statistical mechanics-- is examined in detail. The possibility of a description of it or part of it by a field theory is discussed.

Elementary particle physics and fundamental interactions (J.-M. Gérard, F. Maltoni, J. Pestieau, C. Ringeval, J. Weyers)

• Non-perturbative effects: We study non-perturbative effects induced by strong interactions in electroweak processes to understand CP violation. The tools include 1/N expansion, chiral perturbation, vector dominance, dispersion relations, operator product expansion and sum rules. We consider both light and heavy hadron decays.
• Physics at LHC: We focus on the Higgs sector, the most controversial part of the standard model, and study various extensions to understand the mass spectrum of quarks and leptons.
• General relativity and cosmology: We study the possibility of testing Einstein's theory of gravity at cosmological scales.

History of science (P. Radelet)

• Edition of the complete works of the Bernoulli family: The complete edition of the works (coordinated from LLN) and the correspondence (coordinated from Basel) of the physicists and mathematicians of the Bernoulli family proceeds under the general supervision of D. Speiser. Fourteen volumes have been published, out the 45 being planned.
• Interfaculty study center in history of science: This center is the meeting point of all those who have an interest in the history of science on the Louvain-la-Neuve campus. It organizes a biweekly seminar throughout the academic year, on a theme that varies from year to year. The Center publishes the "Réminisciences" collection, which gathers colloquium proceedings, seminar talks and works from the members.