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2011 Fiscal Year Final Research Report

A research on noncommutative functional identities and their Geometry by deformation quantization

Research Project

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Project/Area Number 21540096
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo University of Science

Principal Investigator

YOSHIOKA Akira  東京理科大学, 理学部, 教授 (40200935)

Co-Investigator(Renkei-kenkyūsha) OMORI Hideki  東京理科大学, 理工学部, 嘱託教授 (20087018)
MAEDA Yoshiaki  慶応義塾大学, 理工学部, 教授 (40101076)
MIYAZAKI Naoya  慶応義塾大学, 経済学部, 教授 (50315826)
Project Period (FY) 2009 – 2011
Keywords複素解析幾何学 / 変形量子化 / 非可換関数論 / 非可換幾何学 / 量子化 / 数理物理学 / 力学的幾何学 / 幾何学と物理学
Research Abstract

Star products are given by means of complex matrices, which are extension of typical star products in physics such as Moyal products. Jacobi theta functions are expressed by means of star exponential of linear functions, and fundamental identities are given by star product expressions. As an application of star exponentials of quadratic functions, we study the spectrum of MIC-Kepler problem in terms of star product algebra.

  • Research Products

    (13 results)

All 2012 2011 2010 2009 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (5 results) Book (3 results)

  • [Journal Article] Star product and its application to the MIC-Kepler problem2012

    • Author(s)
      Tomoyo Kanazawa, Akira Yoshioka
    • Journal Title

      Journal of Geometry and Symmetry in Physics

      Volume: 25 Pages: 57-75

    • Peer Reviewed
  • [Journal Article] Star Products and Applications2010

    • Author(s)
      Mari Iida, Akira Yoshioka
    • Journal Title

      Journal of Geometry and Physics

      Volume: 20 Pages: 49-56

    • Peer Reviewed
  • [Journal Article] Star Products and Theta Functions2010

    • Author(s)
      Akira Yoshioka
    • Journal Title

      AIP proceedings

      Volume: 1307 Pages: 203-208

    • Peer Reviewed
  • [Journal Article]2010

    • Author(s)
      Toshio Tomihisa, Akira Yoshioka
    • Journal Title

      Journal of Geometry and Physics

      Volume: 19 Pages: 99-111

    • Peer Reviewed
  • [Journal Article] Examples of star exponentials2009

    • Author(s)
      Akira Yoshioka
    • Journal Title

      AIP conference proceedings

      Volume: 1191 Pages: 188-193

    • Peer Reviewed
  • [Presentation] Star products and its application to MIC Kepler problem2011

    • Author(s)
      Akira Yoshioka
    • Organizer
      XIIIth international conference on geometry, integrability and quantization
    • Place of Presentation
      Varna(Bulgaria)
    • Year and Date
      2011-06-03
  • [Presentation] Star products and its applications2010

    • Author(s)
      Akira Yoshioka
    • Organizer
      XXIX workshop on geometric methods in physics
    • Place of Presentation
      Bialowieza(Poland)
    • Year and Date
      2010-06-28
  • [Presentation] Star exponential calculus2010

    • Author(s)
      Akira Yoshioka
    • Organizer
      XIth international conference on geometry, integrability and quantization
    • Place of Presentation
      Varna(Bulgaria)
    • Year and Date
      2010-06-05
  • [Presentation] A family of star products and star exponentials2009

    • Author(s)
      Akira Yoshioka
    • Organizer
      XIth international conference on Geometry, integrability and quantization
    • Place of Presentation
      Varna(Bulgaria)
    • Year and Date
      2009-06-05
  • [Presentation] Examples of star exponential functions

    • Author(s)
      Akira Yoshioka
    • Organizer
      XXXVIIIth workshop on geometric methods in physics
    • Place of Presentation
      Bialowieza(Poland)
  • [Book] Nonlinear and noncommutative mathematics, New developments and applications in quantum physics2010

    • Author(s)
      M. Norbert Hounkonnou, Akira Yoshioka
    • Total Pages
      318
    • Publisher
      Hindwai Publishing corporation
  • [Book] Proceedings of the international conference on geometry, integrability and quantization XI2010

    • Author(s)
      Ivailo Mladenov, Akira Yoshioka
    • Total Pages
      232
    • Publisher
      Bulgarian Scientific Publishers
  • [Book] Proceedings of the international conference on geometry, integrability and quantization X2009

    • Author(s)
      Ivailo Mladenov, Akira Yoshioka
    • Total Pages
      288
    • Publisher
      Bulgarian Scientific Publishers

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Published: 2013-07-31  

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