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Quantum and Non-Commutative Analysis

Past, Present and Future Perspectives

  • Book
  • © 1993

Overview

Editors:
  1. Huzihiro Araki

    1. Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan

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  2. Keiichi R. Ito

    1. Department of Mathematics and Information, College of Liberal Arts, Kyoto University, Sakyo-ku, Yoshida Kyoto 606, Japan

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  3. Akitaka Kishimoto

    1. Department of Mathematics Faculty of Science, Hokkaido University, Sapporo 060, Japan

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  4. Izumi Ojima

    1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

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Part of the book series: Mathematical Physics Studies (MPST, volume 16)

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xii
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  2. Quantum Field Theory

    1. Front Matter

      Pages 1-1
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    2. Local Quantum Physics and Beyond

      • Rudolf Haag
      Pages 3-10

    3. A Non-commuting Realization of Minkowski Space

      • H. J. Borchers
      Pages 11-30

    4. Goldstone’s Theorem Revisited

      • John E. Roberts
      Pages 31-39

    5. Global Observables in Local Quantum Physics

      • Klaus Fredenhagen
      Pages 41-51

    6. State of the art of Alain Connes’ version of the standard model

      • D. Kastler
      Pages 53-71

    7. Supersymmetric Extension of Quantum Scalar Field Theories

      • Asao Arai
      Pages 73-90

  3. Statistical and Solid State Physics

    1. Front Matter

      Pages 91-91
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    2. Optimal Two—Uniform Convexity and Fermion Hypercontractivity

      • Eric A. Carlen, Elliott H. Lieb
      Pages 93-111

    3. Renormalization Group and Nonlinear PDE’s

      • J. Bricmont, A. Kupiainen
      Pages 113-118

    4. Random Walk Rperesentations and Mayer Expansion

      • Keiichi R. Ito
      Pages 119-135

    5. The Free-energy Theorem

      • R. F. Streater
      Pages 137-147

    6. Dynamical Entropy of Quasi-local Algebras

      • Yong Moon Park
      Pages 149-165

    7. The Weak Coupling Limit for a Fermi Gas in a Random Potential

      • L. J. Landau
      Pages 167-178

    8. The Gap Labelling Theorem: the case of Automatic Sequences

      • Jean Bellissard
      Pages 179-181

    9. Operator Algebra Approach to Soluble Models of Quantum Spin Lattice Systems

      • Huzihiro Araki
      Pages 183-196

    10. On Conservation Laws of the XY Model

      • Taku Matsui
      Pages 197-204

  4. Quantum Groups

    1. Front Matter

      Pages 205-205
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    2. Reflection Equation Algebras and Quantum Groups

      • P. P. Kulish
      Pages 207-220
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Keywords

About this book

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 Ap­ proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Editors and Affiliations

  • Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan

    Huzihiro Araki

  • Department of Mathematics and Information, College of Liberal Arts, Kyoto University, Sakyo-ku, Yoshida Kyoto 606, Japan

    Keiichi R. Ito

  • Department of Mathematics Faculty of Science, Hokkaido University, Sapporo 060, Japan

    Akitaka Kishimoto

  • Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Izumi Ojima

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