• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Noncommutative functional identites with non formal deformation quantization and its application

Research Project

Project/Area Number 24540097
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
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, 教授 (20087018)
MAEDA Yoshiaki  東北大学, 理学部, 教授 (40101076)
MIYAZAKI Naoya  慶應義塾大学, 経済学部, 教授 (50315826)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords変形量子化 / シンプレクティック幾何学 / ポアソン幾何学 / 非可換幾何学 / 量子化 / 力学 / 接触幾何学 / 複素解析幾何 / シンプレクティック・ポアソン幾何学 / 力学的幾何 / 複素解析
Outline of Final Research Achievements

We consider non-formal deformation quantizaztion. In the obtained star product aligebra, we consider star exponntaials. Using the star exponentials, we can construct certain noncommutative functional identites. As an application, we investigate a concrete MIC-Kepler problem, its eigenvalues, and also its noncommutative symplectic reduction, with non formal star products. Based on the investitation on the MIC-Kepler problem,we extend the noncommutative reduction to general situation with S1 symmetry group.
Using star exponentials,we also obtain vacumms, with which we can obtain
representation of non-formal star product algebras.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (18 results)

All 2015 2014 2013 2012

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (11 results) (of which Invited: 7 results) Book (2 results)

  • [Journal Article] Deformation of expressions for elements of an algebra2014

    • Author(s)
      Hideki Omori, Yoshiaki Maeda, Naoya Miyazaki, Akira Yoshioka
    • Journal Title

      Symplectic, Poisson, and Noncommutative Geometry, Mathematical Sciences Research Institute Publications

      Volume: 62 Pages: 170-209

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An S^1 reduction of non-formal star product2014

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

      Geometry, integrability and quantization

      Volume: 15

    • DOI

      10.7546/giq-15-2014-162-172

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An S^1-reduction of non-formal star product2014

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

      Proceedings of fourteenth international conference Geometry, Integrability and Quantization

      Volume: 14

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Green's function, wavefunction and Wigner function of the MIC-Kepler problem2013

    • Author(s)
      Tomoyo Kanazawa
    • Journal Title

      Journal of geometry and symmetry in physics

      Volume: 30 Pages: 63-73

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Star products and certain star functions2013

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

      Geometric methods in Physics. XXXI Workshop 2012, Trends in Mathematics

      Volume: 1

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Star product and Weyl manifold2015

    • Author(s)
      Akira Yoshioka
    • Organizer
      Current Problems in Theoretical Physics XXI Edition
    • Place of Presentation
      Vietri, Italy
    • Year and Date
      2015-03-28 – 2015-03-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Star product and application2015

    • Author(s)
      吉岡 朗
    • Organizer
      (非)可換代数とトポロジー
    • Place of Presentation
      松本市,信州大学
    • Year and Date
      2015-02-13 – 2015-02-15
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Star functions, example and application2014

    • Author(s)
      Akira Yoshioka
    • Organizer
      XXXIII Workshop on geometric methods in physics
    • Place of Presentation
      Bialowieza, Poland
    • Year and Date
      2014-06-29 – 2014-07-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Star product and star functions2014

    • Author(s)
      Akira Yoshioka
    • Organizer
      The sixteenth international conference on Geometry, integrability and quantization
    • Place of Presentation
      Varna, Bulgaria
    • Year and Date
      2014-06-06 – 2014-06-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Star product and its application2014

    • Author(s)
      Akira Yoshioka
    • Organizer
      International Conference Symmetry Methods, Applications, and Related Fields celebrating the work of Professor George W. Bluman
    • Place of Presentation
      Vancouver, Canada, Univeristy of British Columbia
    • Year and Date
      2014-05-13 – 2014-05-16
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Star products and star exponentials2013

    • Author(s)
      Akira Yoshioka
    • Organizer
      The fifteenth international conference on Geometry, Integrability and Quantization
    • Place of Presentation
      Varna, Bulgaria
    • Related Report
      2013 Research-status Report
  • [Presentation] Star products, star exponentials and applications2013

    • Author(s)
      Akira Yoshioka
    • Organizer
      XXXII Workship on geometric methods in physics
    • Place of Presentation
      Bialowieza, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] Star積について2013

    • Author(s)
      吉岡 朗
    • Organizer
      場の数理とトポロジー
    • Place of Presentation
      信州大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Star products-formal and nonformal2012

    • Author(s)
      Akir Yoshioka
    • Organizer
      XIVth international conference, Geometry, Integrability and Quantization
    • Place of Presentation
      Varna, Bulgaria
    • Related Report
      2012 Research-status Report
  • [Presentation] Star products-formal extension and nonformal extension2012

    • Author(s)
      Akira Yoshioka
    • Organizer
      XXXI Workshop on Geometric methods in Physics
    • Place of Presentation
      Bialowieza, Poland
    • Related Report
      2012 Research-status Report
  • [Presentation] Star products and star functions2012

    • Author(s)
      Akira Yoshioka
    • Organizer
      International conference: Harmonic analysis on homegeneous spaces and quantization
    • Place of Presentation
      Tambov, Russia
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] Proceedings of fifteenth international conference: Geometry, Integrablity and Quantization2014

    • Author(s)
      Ivilo Mladenov, Andrei Ludu, Akira Yoshioka
    • Total Pages
      321
    • Publisher
      Avangard Prima, Sofia, Bulgaria
    • Related Report
      2014 Annual Research Report
  • [Book] Proceedings of fourteenth international conference; Geometry, Integrability and Quantization 142013

    • Author(s)
      Ivailo Mladenov, Andrei Ludu, Akira Yoshioka ed.
    • Total Pages
      271
    • Publisher
      AvangardPrima, Sofia, Bulgaria
    • Related Report
      2013 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi