Quantum and Non-Commutative Analysis: Past, Present and Future Perspectives by HUZIHIRO ARAKIQuantum and Non-Commutative Analysis: Past, Present and Future Perspectives by HUZIHIRO ARAKI

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

EditorHUZIHIRO ARAKI, Keiichi R. Ito, Akitaka Kishimoto

Paperback | December 8, 2010

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This volume contains the proceedings of two international colloquia held in Japan in 1992. The various contributions by pre-eminent scientists cover the fields of quantum field theory, statistical and solid state physics, quantum groups and subfactors and index theory, and operator algebras and related topics. Together they present an authoritative overview of the latest developments by pioneers in these fields. Most of the contributions are self-contained. For graduate students and researchers in mathematics and mathematical physics.
Title:Quantum and Non-Commutative Analysis: Past, Present and Future PerspectivesFormat:PaperbackDimensions:476 pagesPublished:December 8, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048143349

ISBN - 13:9789048143344

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Table of Contents

Foreword and Preface; H. Araki, K.R. Ito, A. Kishimoto, I. Ojima. Part 1: Quantum Field Theory. 1. Local Quantum Physics and Beyond; R. Haag. 2. A Non-Commuting Realization of Minkowski Space; H.J. Borchers. 3. Goldstone's Theorem Revisited; J.E. Roberts. 4. Global Observables in Local Quantum Physics; K. Fredenhagen. 5. State of the Art of Alain Connes' Version of the Standard Model; D. Kastler. 6. Supersymmetric Extension of Quantum Scalar Field Theories; A. Arai. Part 2: Statistical and Solid State Physics. 7. Optimal Two-Uniform Convexity and Fermion Hypercontractivity; E. Lieb, E. Carlen. 8. Renormalization Group and Nonlinear Media; A. Kupiainen, J. Bricmont. 9. Random Wall Representations and Mayer Expansion; K.R. Ito. 10. The Free Energy Theorem; R.F. Streater. 11. Dynamical Entropy of Quasi-Local Algebras; Y.M. Park. 12. The Weak Coupling Limit for a Fermi Gas in a Random Potential; L.J. Landau. 13. The Gap Labelling Theorem: the Case of Automatic Sequences; J. Bellisard. 14. Operator Algebra Approach to Soluble Models of Quantum Spin Lattice Systems; H. Araki. 15. On Conservation Laws of XY Model; T. Matsui. Part 3: Quantum Groups. 16. Reflection Equation Algebras and Quantum Groups; P.P. Kulish. 17. Quantum Groups, Star Products and Cyclic Cohomology; M. Flato, D. Sternheimer. 18. Quantum Group Symmetry in Conformal Field Theory; K. Gawedzki. 19. Spectrum of an Operator appears in the Quantum SU(1,1) Group; T. Kakehi, K. Ueno, T. Masuda. 20. Takesaki Duality for the Crossed Product by Quantum Groups; Y. Nakagami. Part 4: Subfactors and Index Theory. 21. A New Role of Graph Projections in Index Theory; T. Natsume. 22. Endomorphisms and Automorphisms for Factor Inclusions; M. Choda. 23. Automorphisms in the Irreducible Decomposition of Sectors; H. Kosaki. 24. Fusion Rules and Classification of Subfactors; M. Izumi. 25. Vector Bundles and Bimodules; S. Yamagami. 26. Lattice Structure of Intermediate Subfactors; Y. Watatani. 27. Minimal Index Unimodular Sectors; R. Longo. 28. Subfactors and Conformal Field Theory; J. Evans, Y. Kawahigashi. Part 5: Operator Algebras and Related Topics. 29. A Classification of Certain Simple C*-Algebra; G. Elliott. 30. K-Theoretic Classifications for Certain Real Rank Zero C* Algebras; H. Su. 31. Inductive Limits of Interval Algebras; the Simple Case; K. Thomsen. 32. Operator Algebras and Abstract Duals: Progress and Problems; S. Doplicher. 33. Regular Actions of Compact Groups on Cuntz Algebras; C. Pinzari. 34. Almost Shift Invariant Projections in Infinite Tensor Products; O. Bratteli, D. Evans, A. Kishimoto. 35. Strongly Elliptic and Subelliptic Operators on Lie Groups; D.W. Robinson.