Integrable Systems : From Classical to Quantum

This volume presents the papers based upon lectures given at the 1999 Seminaire de Mathemathiques Superieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development since the 1970s, resulting in new motivation for study in surprisingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a cross-section of work in the area of integrable systems which is presented by some of the leading active researchers in this field.