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From Geometry to Quantum Mechanics

In Honor of Hideki Omori

  • Book
  • © 2007

Overview

Editors:
  1. Yoshiaki Maeda

    1. Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, Japan

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  2. Takushiro Ochiai

    1. Department of Natural Science, Nippon Sports Science University, Tokyo, Japan

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  3. Peter Michor

    1. Facultät für Mathematik, Universität Wein, Wein, Austria

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  4. Akira Yoshioka

    1. Department of Mathematics, Tokyo University of Science, Kagurazaka, Tokyo, Japan

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  • Invited articles in differential geometry and mathematical physics in honor of Hideki Omori
  • Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry
  • Will appeal to graduate students in mathematics and quantum mechanics; also a reference

Part of the book series: Progress in Mathematics (PM, volume 252)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xix
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  2. Global Analysis and Infinite-Dimensional Lie Groups

    1. Front Matter

      Pages 1-1
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    2. Aspects of Stochastic Global Analysis

      • K. D. Elworthy
      Pages 3-24

    3. A Lie Group Structure for Automorphisms of a Contact Weyl Manifold

      • Naoya Miyazaki
      Pages 25-44

  4. Symplectic Geometry and Poisson Geometry

    1. Front Matter

      Pages 91-91
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    2. The Integration Problem for Complex Lie Algebroids

      • Alan Weinstein
      Pages 93-109

    3. Reduction, Induction and Ricci Flat Symplectic Connections

      • Michel Cahen, Simone Gutt
      Pages 111-129

    4. Local Lie Algebra Determines Base Manifold

      • Janusz Grabowski
      Pages 131-145

    5. Lie Algebroids Associated with Deformed Schouten Bracket of 2-Vector Fields

      • Kentaro Mikami, Tadayoshi Mizutani
      Pages 147-160

    6. Parabolic Geometries Associated with Differential Equations of Finite Type

      • Keizo Yamaguchi, Tomoaki Yatsui
      Pages 161-209

  5. Quantizations and Noncommutative Geometry

    1. Front Matter

      Pages 211-211
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    2. Toward Geometric Quantum Theory

      • Hideki Omori
      Pages 213-251

    3. Resonance Gyrons and Quantum Geometry

      • Mikhail Karasev
      Pages 253-275

    4. A Secondary Invariant of Foliated Spaces and Type IIIλ von Neumann Algebras

      • Hitoshi Moriyoshi
      Pages 277-286

    5. The Geometry of Space-Time and Its Deformations from a Physical Perspective

      • Daniel Sternheimer
      Pages 287-301
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Keywords

About this book

Hideki Omori is widely recognized as one of the world’s most creative and original mathematicians. This volume is dedicated to Hideki Omori on the occasion of his retirement from Tokyo University of Science. His retirement was also celebrated in April 2004 with an in?uential conference at the Morito Hall of Tokyo University of Science. Hideki Omori was born in Nishionmiya, Hyogo prefecture, in 1938 and was an undergraduate and graduate student at Tokyo University, where he was awarded his Ph.D degree in 1966 on the study of transformation groups on manifolds [3], which became one of his major research interests. He started his ?rst research position at Tokyo Metropolitan University. In 1980, he moved to Okayama University, and then became a professor of Tokyo University of Science in 1982, where he continues to work today. Hideki Omori was invited to many of the top international research institutions, including the Institute for Advanced Studies at Princeton in 1967, the Mathematics Institute at the University of Warwick in 1970, and Bonn University in 1972. Omori received the Geometry Prize of the Mathematical Society of Japan in 1996 for his outstanding contributions to the theory of in?nite-dimensional Lie groups.

Editors and Affiliations

  • Department of Mathematics, Faculty of Science and Technology, Keio University, Hiyoshi, Yokohama, Japan

    Yoshiaki Maeda

  • Department of Natural Science, Nippon Sports Science University, Tokyo, Japan

    Takushiro Ochiai

  • Facultät für Mathematik, Universität Wein, Wein, Austria

    Peter Michor

  • Department of Mathematics, Tokyo University of Science, Kagurazaka, Tokyo, Japan

    Akira Yoshioka

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