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Quantum and Non-Commutative Analysis : Past, Present and Future Perspectives - Huzihiro Araki

Quantum and Non-Commutative Analysis

Past, Present and Future Perspectives

By: Huzihiro Araki (Editor), Keiichi R. Ito (Editor), Akitaka Kishimoto (Editor), Izumi Ojima (Editor)

Hardcover Published: 30th November 1993
ISBN: 9780792325321
Number Of Pages: 464

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In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group ApĀ­ proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Foreword
Preface
Local Quantum Physics and Beyondp. 3
A Non-commuting Realization of Minkowski Spacep. 11
Goldstone's Theorem Revisitedp. 31
Global Observables in Local Quantum Physicsp. 41
State of the Art of Alain Connes' Version of the Standard Modelp. 53
Supersymmetric Extension of Quantum Scalar Field Theoriesp. 73
Optimal Two-Uniform Convexity and Fermion Hypercontractivityp. 93
Renormalization Group and Non-linear Mediap. 113
Random Walk Representations and Mayer Expansionp. 119
The Free-energy Theoremp. 137
Dynamical Entropy of Quasi-local Algebrasp. 149
The Weak Coupling Limit for a Fermi Gas in a Random Potentialp. 167
The Gap Labelling Theorem: the Case of Automatic Sequencesp. 179
Operator Algebra Approach to Soluble Models of Quantum Spin Lattice Systemsp. 183
On Conservation Laws of the XY Modelp. 197
Reflection Equation Algebras and Quantum Groupsp. 207
Quantum Groups, Star Products and Cyclic Cohomologyp. 221
Quantum Group Symmetry in Conformal Field Theoryp. 239
Spectrum of an Operator Appears in the Quantum Su(1,1) Groupp. 253
Takesaki Duality for the Crossed Product by Quantum Groupsp. 263
A New Role of Graph Projections in Index Theoryp. 285
Endomorphisms and Automorphisms for Factor Inclusionsp. 291
Automorphisms in the Irreducible Decomposition of Sectorsp. 305
Fusion Rules and Classification of Subfactorsp. 317
Vector Bundles and Bimodulesp. 321
Lattice Structure of Intermediate Subfactorsp. 331
Minimal Index Unimodular Sectorsp. 335
Subfactors and Conformal Field Theoryp. 341
A Classification of Certain Simple C*-Algebrap. 373
K-Theoretic Classifications for Certain Real Rank Zero C* algebrasp. 387
Inductive Limits of Interval Algebras The Simple Casep. 399
Operator Algebras and Abstract Duals: Progress and Problemsp. 405
Regular Actions of Compact Groups on Cuntz Algebrasp. 419
Almost Shift Invariant Projections in Infinite Tensor Productsp. 427
Strongly Elliptic and Subelliptic Operators on Lie Groupsp. 435
Postscriptsp. 455
List of Speakersp. 461
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792325321
ISBN-10: 079232532X
Series: Mathematical Physics Studies
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 464
Published: 30th November 1993
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.69
Weight (kg): 0.84

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