Noncommutative Differential Geometry and Its Applications to Physics

Proceedings of the Workshop at Shonan, Japan, June 1999

  • Yoshiaki Maeda
  • Hitoshi Moriyoshi
  • Hideki Omori
  • Daniel Sternheimer
  • Tatsuya Tate
  • Satoshi Watamura

Part of the Mathematical Physics Studies book series (MPST, volume 23)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Christian Duval, Pierre B. A. Lecomte, Valentin Ovsienko
    Pages 1-12
  3. Olivier Grandjean
    Pages 31-48
  4. Alexandre Kabanov, Takashi Kimura
    Pages 63-98
  5. Akishi Kato
    Pages 99-121
  6. Toshikazu Natsume
    Pages 155-167
  7. Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka
    Pages 169-186
  8. Simon G. Scott, Krzysztof P. Wojciechowski
    Pages 187-215
  9. Pavol Ševera
    Pages 217-226
  10. Back Matter
    Pages 307-308

About this book


Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments.
However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium.
Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.


D-branes Lattice gauge theory Poisson groupoids differential geometry manifold noncommutative differential geometry operad theory quantization problems

Editors and affiliations

  • Yoshiaki Maeda
    • 1
  • Hitoshi Moriyoshi
    • 1
  • Hideki Omori
    • 2
  • Daniel Sternheimer
    • 3
  • Tatsuya Tate
    • 1
  • Satoshi Watamura
    • 4
  1. 1.Keio UniversityYokohamaJapan
  2. 2.Science University of TokyoNodaJapan
  3. 3.CNRS and Université de BourgogneDijonFrance
  4. 4.Tohoku UniversitySendaiJapan

Bibliographic information