Contemporary Mathematics 1998; 195 pp; softcover Volume: 214 ISBN10: 082180684X ISBN13: 9780821806845 List Price: US$50 Member Price: US$40 Order Code: CONM/214
 This book presents the proceedings of a 1996 Joint Summer Research Conference sponsored by AMSIMSSIAM on "Quantization" held at Mount Holyoke College (Northampton, MA). The purpose of the conference was to bring together researchers focusing on various mathematical aspects of quantization. In the early work of Weyl and von Neumann at the beginning of the quantum era, the setting for this enterprise was operators on Hilbert space. This setting has been expanded, especially over the past decade, to involve \(C^*\)algebrasnoncommutative differential geometry and noncommutative harmonic analysisas well as more general algebras and infinitedimensional manifolds. The applications now include quantum field theory, notable conformal and topological field theories related to quantization of moduli spaces, and constructive quantum field theory of supersymmetric models and condensed matter physics (the fractional quantum Hall effect in particular). The spectrum of research interests which significantly intersects the topic of quantization is unusually broad, including, for example, pseudodifferential analysis, the representation theory of Lie groups and algebras (including infinitedimensional ones), operator algebras and algebraic deformation theory. The papers in this collection originated with talks by the authors at the conference and represent a strong crosssection of the interests described above. Readership Graduate students, research mathematicians, and physicists interested in quantum theory. Table of Contents  J. Arazy and H. Upmeier  Discrete series representations and integration over boundary orbits of symmetric domains
 D. Borthwick  Microlocal techniques for semiclassical problems in geometric quantization
 J. Dimock  A nonGaussian fixed point for the renormalization group
 B. C. Hall  Quantum mechanics in phase space
 T. J. Hodges  Nonstandard quantum groups associated to certain BelavinDrinfeld triples
 S. Klimek and A. Leśniewski  Ergodic theorems for quantum Kronecker flows
 S. Klimek and A. Leśniewski  Quantum maps
 G. W. Mackey  The relationship between classical mechanics and quantum mechanics
 G. Nagy  Deformation quantization and \(K\)theory
 J. H. Przytycki  A \(q\)analogue of the first homology group of a 3manifold
 I. Segal  Constructive nonlinear quantum field theory in four spacetime dimensions
 A. J. L. Sheu  Groupoids and quantization
 A. Unterberger  Quantization, symmetries, and relativity
 A. A. Voronov  Quantizing Poisson manifolds
