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Noncommutative Differential Geometry and Its Applications to Physics

Proceedings of the Workshop at Shonan, Japan, June 1999

  • Conference proceedings
  • © 2001

Overview

Editors:
  1. Yoshiaki Maeda

    1. Keio University, Yokohama, Japan

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  2. Hitoshi Moriyoshi

    1. Keio University, Yokohama, Japan

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  3. Hideki Omori

    1. Science University of Tokyo, Noda, Japan

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  4. Daniel Sternheimer

    1. CNRS and Université de Bourgogne, Dijon, France

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  5. Tatsuya Tate

    1. Keio University, Yokohama, Japan

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  6. Satoshi Watamura

    1. Tohoku University, Sendai, Japan

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

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Table of contents (15 papers)

  1. Front Matter

    Pages i-viii
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  2. Methods of Equivariant Quantization

    • Christian Duval, Pierre B. A. Lecomte, Valentin Ovsienko
    Pages 1-12

  3. Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory

    • Takanori Fujiwara, Hiroshi Suzuki, Ke Wu
    Pages 13-30

  4. Geometrical Structures on Noncommutative Spaces

    • Olivier Grandjean
    Pages 31-48

  5. A Relation Between Commutative and Noncommutative Descriptions of D-Branes

    • Nobuyuki Ishibashi
    Pages 49-61

  6. Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0

    • Alexandre Kabanov, Takashi Kimura
    Pages 63-98

  7. D-Brane Actions on Kähler Manifolds

    • Akishi Kato
    Pages 99-121

  8. On The Projective Classification of the Modules of Differential Operators on ℝm

    • Pierre B. A. Lecomte
    Pages 123-129

  9. An Interpretation of the Schouten-Nijenhuis Bracket

    • Kentaro Mikami
    Pages 131-143

  10. Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators

    • Naoya Miyazaki
    Pages 145-154

  11. C*-Algebraic Deformation and Index Theory

    • Toshikazu Natsume
    Pages 155-167

  12. Singular Systems of Exponential Functions

    • Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka
    Pages 169-186

  13. Determinants of Elliptic Boundary Problems in Quantum Field Theory

    • Simon G. Scott, Krzysztof P. Wojciechowski
    Pages 187-215

  14. On Geometry of Non-Abelian Duality

    • Pavol Ševera
    Pages 217-226

  15. Weyl Calculus and Wigner Transform on the Poincaré Disk

    • Tatsuya Tate
    Pages 227-243

  16. Lectures on Graded Differential Algebras and Noncommutative Geometry

    • Michel Dubois-Violette
    Pages 245-306

  17. Back Matter

    Pages 307-308
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Keywords

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.

Editors and Affiliations

  • Keio University, Yokohama, Japan

    Yoshiaki Maeda, Hitoshi Moriyoshi, Tatsuya Tate

  • Science University of Tokyo, Noda, Japan

    Hideki Omori

  • CNRS and Université de Bourgogne, Dijon, France

    Daniel Sternheimer

  • Tohoku University, Sendai, Japan

    Satoshi Watamura

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