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

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.