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Perspectives on quantization : proceedings of the 1996 AMS-IMS-SIAM Joint Summer Research Conference, July 7-11, 1996, Mt. Holyoke College / Lewis A. Coburn, Marc A. Rieffel, editors.
- Format:
- Book
- Conference/Event
- Author/Creator:
- AMS-IMS-SIAM Joint Summer Research Conference, Corporate Author.
- Conference Name:
- AMS-IMS-SIAM Joint Summer Research Conference, issuing body.
- AMS-IMS-SIAM Joint Summer Research Conference
- Series:
- Contemporary mathematics (American Mathematical Society) ; 214.
- Contemporary mathematics, 0271-4132 ; 214
- Language:
- English
- Subjects (All):
- Quantum theory--Mathematics--Congresses.
- Quantum theory.
- Quantum field theory--Congresses.
- Quantum field theory.
- Physical Description:
- 1 online resource (210 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [1998]
- Language Note:
- English
- Summary:
- 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 this 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.
- Contents:
- ""Contents""; ""List of participants""; ""Preface""; ""Discrete series representations and integration over boundary orbits of symmetric domains""; ""Microlocal techniques for semiclassical problems in geometric quantization""; ""A non-Gaussian fixed point for the renormalization group""; ""Quantum mechanics in phase space""; ""1. History and background""; ""2. The holomorphic function representation""; ""3. The complex group as phase space""; ""4. An inversion formula""; ""5 . An uncertainty principle""; ""6. Toeplitz operators""; ""7. Comparison with geometric quantization""
- ""Nonstandard quantum groups associated to certain Belavin-Drinfeld triples""""Ergodic theorems for quantum Kronecker flows""; ""Quantum maps""; ""The relationship between classical mechanics and quantum mechanics""; ""Deformation quantization and K -theory""; ""A q-analogue of the first homology group of a 3-manifold""; ""Constructive non-linear quantum field theory in four space-time dimensions""; ""Groupoids and quantization""; ""Quantization, symmetries, and relativity""; ""Quantizing Poisson manifolds""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-7806-9
- 0-8218-5550-6
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