Perspectives on quantization : proceedings of a 1996 AMS-IMS-SIAM Joint Summer Research Conference, July 7-11, 1996, Mt. Holyoke College
著者
書誌事項
Perspectives on quantization : proceedings of a 1996 AMS-IMS-SIAM Joint Summer Research Conference, July 7-11, 1996, Mt. Holyoke College
（Contemporary mathematics, v. 214）
American Mathematical Society, c1998
- : pbk
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Discrete series representations and integration over boundary orbits of symmetric domains by J. Arazy and H. Upmeier Microlocal techniques for semiclassical problems in geometric quantization by D. Borthwick A non-Gaussian fixed point for the renormalization group by J. Dimock Quantum mechanics in phase space by B. C. Hall Nonstandard quantum groups associated to certain Belavin-Drinfeld triples by T. J. Hodges Ergodic theorems for quantum Kronecker flows by S. Klimek and A. Lesniewski Quantum maps by S. Klimek and A. Lesniewski The relationship between classical mechanics and quantum mechanics by G. W. Mackey Deformation quantization and $K$-theory by G. Nagy A $q$-analogue of the first homology group of a 3-manifold by J. H. Przytycki Constructive non-linear quantum field theory in four space-time dimensions by I. Segal Groupoids and quantization by A. J. L. Sheu Quantization, symmetries, and relativity by A. Unterberger Quantizing Poisson manifolds by A. A. Voronov.
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