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Softcover ISBN:  9780821806845 
Product Code:  CONM/214 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
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Product Code:  CONM/214.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821806845 
eBook ISBN:  9780821878064 
Product Code:  CONM/214.B 
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Book DetailsContemporary MathematicsVolume: 214; 1998; 195 ppMSC: Primary 81
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 \(C^*\)algebras—noncommutative differential geometry and noncommutative harmonic analysis—as 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.
ReadershipGraduate students, research mathematicians, and physicists interested in quantum theory.

Table of Contents

Articles

Jonathan Arazy and Harald Upmeier — Discrete series representations and integration over boundary orbits of symmetric domains [ MR 1601205 ]

David Borthwick — Microlocal techniques for semiclassical problems in geometric quantization [ MR 1601209 ]

J. Dimock — A nonGaussian fixed point for the renormalization group [ MR 1601213 ]

Brian C. Hall — Quantum mechanics in phase space [ MR 1601217 ]

Timothy J. Hodges — Nonstandard quantum groups associated to certain BelavinDrinfeld triples [ MR 1601221 ]

Sławomir Klimek and Andrzej Leśniewski — Ergodic theorems for quantum Kronecker flows [ MR 1601225 ]

Sławomir Klimek and Andrzej Leśniewski — Quantum maps [ MR 1601229 ]

George W. Mackey — The relationship between classical mechanics and quantum mechanics [ MR 1601233 ]

Gabriel Nagy — Deformation quantization and $K$theory [ MR 1601237 ]

Józef H. Przytycki — A $q$analogue of the first homology group of a $3$manifold [ MR 1601241 ]

Irving Segal — Constructive nonlinear quantum field theory in four spacetime dimensions [ MR 1601245 ]

Albert J. L. Sheu — Groupoids and quantization [ MR 1601249 ]

André Unterberger — Quantization, symmetries and relativity [ MR 1601253 ]

Alexander A. Voronov — Quantizing Poisson manifolds [ MR 1601257 ]


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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 \(C^*\)algebras—noncommutative differential geometry and noncommutative harmonic analysis—as 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.
Graduate students, research mathematicians, and physicists interested in quantum theory.

Articles

Jonathan Arazy and Harald Upmeier — Discrete series representations and integration over boundary orbits of symmetric domains [ MR 1601205 ]

David Borthwick — Microlocal techniques for semiclassical problems in geometric quantization [ MR 1601209 ]

J. Dimock — A nonGaussian fixed point for the renormalization group [ MR 1601213 ]

Brian C. Hall — Quantum mechanics in phase space [ MR 1601217 ]

Timothy J. Hodges — Nonstandard quantum groups associated to certain BelavinDrinfeld triples [ MR 1601221 ]

Sławomir Klimek and Andrzej Leśniewski — Ergodic theorems for quantum Kronecker flows [ MR 1601225 ]

Sławomir Klimek and Andrzej Leśniewski — Quantum maps [ MR 1601229 ]

George W. Mackey — The relationship between classical mechanics and quantum mechanics [ MR 1601233 ]

Gabriel Nagy — Deformation quantization and $K$theory [ MR 1601237 ]

Józef H. Przytycki — A $q$analogue of the first homology group of a $3$manifold [ MR 1601241 ]

Irving Segal — Constructive nonlinear quantum field theory in four spacetime dimensions [ MR 1601245 ]

Albert J. L. Sheu — Groupoids and quantization [ MR 1601249 ]

André Unterberger — Quantization, symmetries and relativity [ MR 1601253 ]

Alexander A. Voronov — Quantizing Poisson manifolds [ MR 1601257 ]