Quantum and Non-Commutative Analysis

Past, Present and Future Perspectives

  • Huzihiro Araki
  • Keiichi R. Ito
  • Akitaka Kishimoto
  • Izumi Ojima

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Quantum Field Theory

  3. Statistical and Solid State Physics

    1. Front Matter
      Pages 91-91
    2. Eric A. Carlen, Elliott H. Lieb
      Pages 93-111
    3. J. Bricmont, A. Kupiainen
      Pages 113-118
    4. R. F. Streater
      Pages 137-147
    5. Yong Moon Park
      Pages 149-165
    6. Taku Matsui
      Pages 197-204
  4. Quantum Groups

    1. Front Matter
      Pages 205-205
    2. Moshé Flato, Daniel Sternheimer
      Pages 221-237
    3. Krzysztof Gawedzki
      Pages 239-251
    4. Tomoyuki Kakehi, Tetsuya Masuda, Kimio Ueno
      Pages 253-261
  5. Subfactors and Index Theory

    1. Front Matter
      Pages 283-283
    2. Yamagami Shigeru
      Pages 321-329
    3. Yasuo Watatani
      Pages 331-333
    4. Roberto Longo
      Pages 335-340
    5. David E. Evans, Yasuyuki Kawahigashi
      Pages 341-369
  6. Operator Algebras and Related Topics

    1. Front Matter
      Pages 371-371
    2. George A. Elliott
      Pages 373-385
    3. Ola Bratteli, David E. Evans, Akitaka Kishimoto
      Pages 427-434
  7. Back Matter
    Pages 455-464

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.


Lattice Minkowski space Potential Renormalization group mathematical physics quantum field theory quantum physics

Editors and affiliations

  • Huzihiro Araki
    • 1
  • Keiichi R. Ito
    • 2
  • Akitaka Kishimoto
    • 3
  • Izumi Ojima
    • 4
  1. 1.Research Institute for Mathematical SciencesKyoto UniversitySakyo-ku, KyotoJapan
  2. 2.Department of Mathematics and Information, College of Liberal ArtsKyoto UniversitySakyo-ku, Yoshida Kyoto 606Japan
  3. 3.Department of Mathematics Faculty of ScienceHokkaido UniversitySapporo 060Japan
  4. 4.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4334-4
  • Online ISBN 978-94-017-2823-2
  • Buy this book on publisher's site