Synopses & Reviews
The focus of this volume is on quantum field theory: inegrable theories, statistical systems, and applications to condensed-matter physics. It covers some of the most significant recent advances in theoretical physics at a level accessible to advanced graduate students. The contributions, each by a noted researcher, dicuss such topics as: some remarkable features of integrable Toda field theories (E. Corrigan), properties of a gas of interacting Fermions in a lattice of magnetic ions (J. Feldman &. al.), how quantum groups arise in three-dimensional topological quantum field thory (D. Freed), a method for computing correlation functions of solvable lattice models (T. Miwa), matrix models discussed from the point of view of integrable systems (A. Morozov), localization of path integrals in certain equivariant cohomologies (A. Niemi), Calogero-Moser systems (S. Ruijsenaars), planar gauge theories with broken symmetries (M. de Wild Propitius & F.A. Bais), quantum-Hall fluids (A. Capelli & al.), spectral theory of quantum vortex operators (P.I. Ettinghoff).
Synopsis
The present volume has its source in the CAP-CRM summer school on "Particles and Fields" that was held in Banff in the summer of 1994. Over the years, the Division of Theoretical Physics of the Canadian Associa- tion of Physicists (CAP) has regularly sponsored such schools on various theoretical and experimental topics. In 1994, the Centre de Recherches Mathematiques (CRM) lent its support to the event. This institute, located in Montreal, is one of Canada's national research centers in the mathe- matical sciences. Its mandate includes the organization of scientific events across Canada and since 1994 the CRM has been holding a yearly summer school in Banff as part of its thematic program. The summer school, whose lectures are collected here, has thus become a tradition. The focus of the school was integrable theories, matrix models, statistical systems, field theory and its applications to condensed matter physics, as well as certain aspects of algebra, geometry, and topology. This covers some of the most significant advances in modern theoretical physics. The present volume updates and expands these lectures and reflects the high pedagogical level of the school. The first chapter by E. Corrigan describes some of the remarkable fea- tures of the integrable Toda field theories which are associated with affine Dynkin diagrams. The second chapter by J. Feldman, H. Knorrer, D. Leh- mann, and E.
Table of Contents
Recent Developments in Affine Toda Quantum Theory (E. Corrigan).- A Class of Fermi Liquids (J. Feldman, H. Knorrer, D. Lehmann, E. Trubowitz).- Quantum Groups from Path Integrals (Daniel S. Freed).- Half-Transfer Matrices in Solvable Lattice Models (Tetsuji Miwa).- Matrix Models as Integrable Systems (A. Morozov).- Four Lectures on Localization, Equivariant Cohomology, and Integration Formulas (Antti J. Niemi).- Systems of Calogero-Moser Type (S.N.M. Ruijsenaars).- Discrete Gauge Theories (Mark de Wild Propitius, F. Alexander Bais).- Quantum Hall Fluids as W1+Infinity Minimal Models (Andrea Cappelli, Carlo A. Trugenberger, Guillermo R. Zemba).- On Spectral Theory of Quantum Vertex Operators (Pavel I. Etingof).