Encyclopedia of Mathematical Physics

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Francoise, Universite Pierre et Marie Curie, Paris, France Gregory L.Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit www.info.sciencedirect.com. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.

Table of Contents:
Classical, Conformal and Topological Field Theory Classical Mechanics Condensed Matter Physics and Optics Differential Geometry Dirac Operators Dynamical Systems Fluid Dynamics Functional Analysis and Variational Techniques Gauge Theory General Relativity Integrable Systems Lie Groups and Lie Algebras Many Particle Systems Noncommutative Geometry Partial Differential Equations and ODEs Path Integrals and Functional Integrals Perturbation Theory Quantization Techniques Quantum Field Theory Quantum Gravity Quantum Groups Quantum Information and Computation Quantum Mechanics Renormalization Scattering Theory Semi-classical Approximations Singularity Theory Statistical Mechanics Stochastic Methods String Theory and M-Theory Supersymmetry Symmetry and Conservation Laws Symplectic Techniques Topological Methods

About the Author :
Professor Françoise graduated in Mathematics and in Physics from Grenoble University, France in 1975. He is currently professor of Mathematics at the Université Pierre et Marie Curie, Paris and a member of the Laboratoire Jacques-Louis Lions after having held a position of chargé de recherches at CNRS. Professor Françoise regularly travels and lectures abroad. He spent one year at IMPA (Rio de Janeiro, Brazil) in 1981 and one year at U.C. Berkeley in 1984. He was associate professor at University of Arizona, Tucson in 1987. Professor Françoise has delivered several series of lectures in Milan, in Rome, at the Banach Centre (Warsaw), at CRM (Montréal) and other institutes. He received the prize “du Fay” from the Académie des Sciences de Paris in 1989. His scientific publications include over eighty articles published in international journals and contributions to several books. His scientific research activity focuses on small oscillations near equilibrium of Hamiltonian systems, singularity theory of functions and vector fields, normal forms and semi-classical analysis, integrable systems, bifurcation theory of dynamical systems, finiteness properties of singular projections of analytic sets, bursting oscillations, synchronization and phase locking of weakly coupled oscillators and isochronous systems. Dr. Gregory L. Naber received all three of his degrees in Mathematics from Carnegie-Mellon University and has since held positions in Pennsylvania, California, Hong Kong and Tennessee. His areas of interest include differential topology and geometry and, most particularly, their interaction with mathematical physics. It is this interaction, and the desire to make it more widely known, appreciated and utilized in the mathematical community that has motivated nearly all of his published work, as well as his involvement with the Encyclopedia of Mathematical Physics. Dr. Tsou Sheung Tsun obtained her B.Sc. in Hong Kong and her Doctorat esSciences in Geneva. She has held research fellowships at Wadham College, Oxford, and at the Mathematical Institute, Oxford, where she is now on the Faculty. Trained both as a mathematician and a physicist, Dr. Tsou has worked in gauge theory, string theory and particle physics. Recently she has concentrated on theoretical problems connected with the generation puzzle, neutrino oscillation and electric-magnetic duality. She is also active in the European Mathematical Society and European Women in Mathematics.

Review :
"This 5-volume encyclopedia contains a very comprehensive collection of articles covering the entire range of mathematical and theoretical physics. The authors of the articles include recognized leaders in their fields, and the essays themselves, each several pages in extent, are more like survey articles than "telegraphic" reviews. To give a sense of the contents, there is a more or less continuous spectrum from physical to mathematical articles. Indeed, some of the entries are devoted to bridging the divide, e.g. "Fourier-Mukai transform in string theory", "Twistor theory: some applications". Much effort was expended in ensuring that the articles would contain information up to the level of present knowledge, which, together with the excellent bibliographies appended to each entry, goes a long way toward ensuring the these volumes will remain a vital source of information and a valuable reference work for some time to come." -in 2007K