This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.

Inhalt

Opening Address; M. Flato. The publications of Guy Rideau. The Problem of Invariants for Lie-Bäcklund Groups; R.L. Anderson, N.H. Ibragimov. Galilean Coherent States and Wavelets; J.-P. Antoine. On the Use of Quantum Algebras in Rotation-Vibration Spectroscopy; R. Barbier, M. Kibler. Invariant Differential Calculus on a Deformation of the Weyl-Heisenberg Algebra; J. Bertrand, M. Irac-Astaud. Noncompact Topological Quantum Groups; F. Bidegain. Symmetric Symplectic Manifolds and Deformation Quantization; P. Bieliavsky, et al. The Conformal Invariance of the Klein-Gordon Equation in 1+1 Dimension; S. de Bièvre, J. Renaud. Compact Topological Quantum Groups; P. Bonneau. Groupes de transformations des variétés statistiques; G. Burdet, M. Perrin. Non-Frustrated Signed Graphs; Ph. Combe, H. Nencka. De l'ubiquité de la condition KMS; G.G. Emch. A Model for QCD in Three Dimensions; C. Frønsdal. Poisson Path Integral Representation of Green Functions for Certain Field Theories; B. Gaveau, et al. Diffeomorphism Group Representations and Nonlinear Quantum Theories; G.G. Goldin. Conditional Symmetries for 1st order Systems of PDES in the Context of the Clairin Method; A.M. Grundland, G. Rideau. Quasistationary Approximation and Gauge Invariance in Classical Electrodynamics; A. Heslot. Graded Poisson Brackets and Field Theory; Y. Kosmann-Schwarzbach. The Basic Lemma in the Theory of Formal Groups; C. Moreno, F. Galvez. Spectra and Generalized Eigenfunctions of the One- and Two-Mode Squeezing Operators in Quantum Optics; B. Nagel. A Higgs-free Model for Fundamental Interactions; M. Pawlowski, R. Raczka. Coupled Hodgkin Huxley Neurons with Stochastic Synaptic Inputs; R. Rodriguez. Initial Data forNon-Linear Evolution Equations and Differentiable Vectors of Group Representations; J.C.H. Simon, E. Taflin. Star Products: Their Ubiquity and Unicity; D. Sternheimer. Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov Equation; I.T. Todorov. Continuous Symmetries of Differential-Difference Equations; P. Winternitz, D. Levi. Processus limités et irréversibilité en mécanique statistique hors d'équilibre; R. Jancel. Allocution de clôture; G. Rideau.