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Perspectives on Quantization
Edited by: Lewis A. Coburn, State University of New York at Buffalo, NY, and Marc A. Rieffel, University of California, Berkeley, CA
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Contemporary Mathematics
1998; 195 pp; softcover
Volume: 214
ISBN-10: 0-8218-0684-X
ISBN-13: 978-0-8218-0684-5
List Price: US$47
Member Price: US$37.60
Order Code: CONM/214
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This book presents the proceedings of a 1996 Joint Summer Research Conference sponsored by AMS-IMS-SIAM 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 \(C^*\)-algebras--noncommutative differential geometry and noncommutative harmonic analysis--as well as more general algebras and infinite-dimensional 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 infinite-dimensional 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 cross-section 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 non-Gaussian fixed point for the renormalization group
  • B. C. Hall -- Quantum mechanics in phase space
  • T. J. Hodges -- Nonstandard quantum groups associated to certain Belavin-Drinfeld 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 3-manifold
  • I. Segal -- Constructive non-linear quantum field theory in four space-time dimensions
  • A. J. L. Sheu -- Groupoids and quantization
  • A. Unterberger -- Quantization, symmetries, and relativity
  • A. A. Voronov -- Quantizing Poisson manifolds
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