**Contemporary Mathematics**

Volume: 214;
1998;
195 pp;
Softcover

MSC: Primary 81;

Print ISBN: 978-0-8218-0684-5

Product Code: CONM/214

List Price: $50.00

Individual Member Price: $40.00

**Electronic ISBN: 978-0-8218-7806-4
Product Code: CONM/214.E**

List Price: $50.00

Individual Member Price: $40.00

# Perspectives on Quantization

Share this page *Edited by *
*Lewis A. Coburn; Marc A. Rieffel*

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.

#### Table of Contents

# Table of Contents

## Perspectives on Quantization

- Contents vii8 free
- List of participants ix10 free
- Preface xi12 free
- Discrete series representations and integration over boundary orbits of symmetric domains 114 free
- Microlocal techniques for semiclassical problems in geometric quantization 2336
- A non-Gaussian fixed point for the renormalization group 3952
- Quantum mechanics in phase space 4760
- Nonstandard quantum groups associated to certain Belavin-Drinfeld triples 6376
- Ergodic theorems for quantum Kronecker flows 7184
- Quantum maps 8194
- The relationship between classical mechanics and quantum mechanics 91104
- Deformation quantization and K -theory 111124
- A q-analogue of the first homology group of a 3-manifold 135148
- Constructive non-linear quantum field theory in four space-time dimensions 145158
- Groupoids and quantization 157170
- Quantization, symmetries, and relativity 169182
- Quantizing Poisson manifolds 189202

#### Readership

Graduate students, research mathematicians, and physicists interested in quantum theory.