Modern Group Theoretical Methods in Physics
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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. Booknews Twenty-eight papers from a conference (Paris, January 1995) held in honor of the retirement of Guy Rideau, include 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. Topics range from pure mathematics to up-to-date applications such as imaging and neuronal models. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Opening AddressThe publications of Guy RideauThe Problem of of Invariants for Lie-Backlund Groups1Galilean Coherent States and Wavelets15On the Use of Quantum Algebras in Rotation-Vibration Spectroscopy27Invariant Differential Calculus on a Deformation of the Weyl-Heisenberg Algebra37Noncompact Topological Quantum Groups51Symmetric Symplectic Manifolds and Deformation Quantization63The Conformal Invariance of the Klein-Gordon Equation in 1+1 Dimension75Compact Topological Quantum Groups87Groupes de Transformations des Varietes Statistiques97Non-Frustrated Signed Graphs105De l'Ubiquite de la Condition KMS115A Model for QCD in Three Dimensions129Poisson Path Integral Representation of Green Functions for Certain Field Theories143Diffeomorphism Group Representations and Nonlinear Quantum Theories157Conditional Symmetries for 1st order Systems of PDES in the Context of the Clairin Method167Quasistationary Approximation and Gauge Invariance in Classical Electrodynamics179Graded Potsson Brackets and Field Theory189The Basic Lemma in the Theory of Formal Groups197Spectra and Generalized Eigenfunctions of the One- and Two-Mode Squeezing Operators in Quantum Optics211A Higgs-free Model for Fundamental Interactions221Coupled Hodgkin Huxley Neurons with Stochastic Synaptic Inputs233Initial Data for Non-Linear Evolution Equations and Differentiable Vectors of Group Representations243Star Products: Their Ubiquity and Unicity255Finite Braid Groups for the SU(2) Knizhnik Zamolodchikov Equation267Continuous Symmetries of Differential-Difference Equations271Processus Limites et Irreversibilite en Mecanique Statistique hors d'Equilibre283Allocution de Cloture315
