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Research on the Field Theory in the Noncommutative Space obtained through the Deformation Quantization and its Application

Research Project

Project/Area Number 13640256
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionTohoku University

Principal Investigator

WATAMURA Satoshi  Tohoku University, Graduate School of Science, Associated professor, 大学院・理学研究科, 助教授 (00201252)

Co-Investigator(Kenkyū-buntansha) ISHIKAWA Hiroshi  Tohoku University, Graduate School of Science, Assistant Professor, 大学院・理学研究科, 助手 (20291247)
Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
KeywordsNoncommutative geometry / Quantum Geometry / Fuzzy Sphere / Fuzzy CPn / Projective Module / Noncommutative Monpole / Matrix Theory / 非可換射影空間 / 非可換インスタント / Nahm duality / ADHM構成 / 非可換インスタントン
Research Abstract

In the string theory it becomes very important to understand the field theory on the noncommutative geometry, since it appears as an effective theory of the D-brane. The essence of the field theory over the noncommutative geometry is considered to appear in the curved space. However, unlike the analysis of the instanton solution over (flat) four-dimensional Euclidian space, the study of the theory on the curved noncommutative space is not so well understood. One origin of this is the lack of typical examples.
Our previous research about the fuzzy sphere gives many interesting aspects from various points of view : It appears as a D-brane configuration in string theory. However, it is also interesting as a regularized theory since it has a chiral fermion structure similar to the lattice case. It is therefore important to find more examples.
In our recent investigation, we have constructed noncommutative CPn by generalizing the fuzzy sphere. The line bundle was constructed in terms of projective modules and we analyzed its topological structure. The differential calculus is defined in a similar way as in the fuzzy sphere case and the noncommutative analogue of the Chern character of the noncommutative CPn is given. In this context it is necessary to understand the meaning of the subsphere in order to perform the integration. It turns out that a certain class of subsphere remains as a subsphere in the commutative limit, and in this case we can evaluate the first Chern number. (Published as hep-th 0404130.)

Report

(5 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (27 results)

All 2005 2004 2003 2001 Other

All Journal Article (12 results) Book (7 results) Publications (8 results)

  • [Journal Article] Monopole Bundles over Fuzzy Complex Projective Spaces2005

    • Author(s)
      U.Carow-Watamura, H.Steinacker, S.Watamura
    • Journal Title

      Journal of Geometry and Physics (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 非可換空間上のゲージ理論2005

    • Author(s)
      綿村 哲
    • Journal Title

      数理物理への誘い 5

      Pages: 143-168

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Gauge Theory on Noncommutataive Space[Japanese]2005

    • Author(s)
      Satoshi Watamura
    • Journal Title

      Introduction to Math.Phys. vol 5

      Pages: 143-168

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Monopole Bundles over Fuzzy Complex Projective Spaces2005

    • Author(s)
      U.Carow-Watamura, H.Steinacker, S.Watamura
    • Journal Title

      Journal of Geometry and Physics (出版予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] TWISTED BOUNDARY STATES IN KAZAMA-SUZUKI MODELS2004

    • Author(s)
      Hiroshi Ishikawa, Taro Tani
    • Journal Title

      Nuclear Physics B678

      Pages: 363-397

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 時空の不確定性と非可換性2004

    • Author(s)
      綿村 哲
    • Journal Title

      数理科学 495

      Pages: 35-40

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Uncertainity of Spacetime and Noncommutativity[Japanese]2004

    • Author(s)
      Satoshi Watamura
    • Journal Title

      Surikagaku vol.495

      Pages: 35-40

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] TWISTED BOUNDARY STATES IN KAZAMA-SUZUKIMODELS2004

    • Author(s)
      Hiroshi Ishikawa, Taro Tani
    • Journal Title

      Nuclear Physics B678

      Pages: 363-397

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Novel construction of boundary states in coset conformal field theories2003

    • Author(s)
      Hiroshi Ishikawa, Taro Tani
    • Journal Title

      Nuclear Physics B649

      Pages: 205-242

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 超弦理論と数学の発展 -時空の新しい描像-2001

    • Author(s)
      綿村 哲
    • Journal Title

      数理科学 462

      Pages: 33-39

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Progress of Superstring and Mathematics -New Picture of Spacetime -[Japanese]2001

    • Author(s)
      Satoshi Watamura
    • Journal Title

      Surikagaku vol.462

      Pages: 33-39

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Monopole Bundles over Fuzzy Complex Projective Spaces

    • Author(s)
      U.Carow-Watamura, H.Steinacker, S.Watamura
    • Journal Title

      Journal of Geometry and Physics (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Quantum Field Theory and Noncommulative Geometry2005

    • Author(s)
      U.Carow-Watamura, Y.Maeda, S.Watamura
    • Total Pages
      297
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Lecture Notes in Physics(662)(Quantum Field Theory and Noncommutative Geometry)2005

    • Author(s)
      Y.Maeda, U.Carow-Watamura, S.Watamura
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Quantum Field Theory and Noncommutative Geometry2005

    • Author(s)
      U.Carow-Watamura, Y.Maeda, S.Watamura
    • Total Pages
      297
    • Publisher
      Springer
    • Related Report
      2004 Annual Research Report
  • [Book] Noncommutative Differential Geometry and Its Application to Physics2001

    • Author(s)
      Y.Maeda, H.Moriyoshi, H.Omori, D.Stemheimer, T.Tate, S.Watamura
    • Total Pages
      306
    • Publisher
      Kuluwer Academic Pbulishers
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Supplement 144, Noncommutative Geometry and String Theory2001

    • Author(s)
      Y.Maeda, S.Watamura
    • Total Pages
      196
    • Publisher
      Progress of Theoretical Physics
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Noncommutative Differential Geometry and Its Application to Physics, Proceedings of the Workshop at Shonan, Japan June 1999.2001

    • Author(s)
      Y.Maeda, H.Moriyoshi, H.Omori, D.Sternheimer, T.Tate, S.Watamura
    • Publisher
      Kuluwer Academic Publishers, Boston/Dordrecht/London
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Progress of Theoretical Physics(Supplement, Vol.144)(Noncommutative Geometry and String theory)2001

    • Author(s)
      Y.Maeda, S.Watamura
    • Publisher
      Progress of Theoretical Physics, Kyoto
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] Hiroshi Ishikawa, Taro Tani: "TWISTED BOUNDARY STATES IN KAZAMA-SUZUKI MODELS"Nuclear Physics. B678. 363-397 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroshi Ishikawa, Taro Tani: "NOVEL CONSTRUCTION OF BOUNDARY STATES IN COSET CONFORMAL FIELD THEORIES"Nuclear Physics. B649. 205-242 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hiroshi Ishikawa, Taro Tani: "NOVEL CONSTRUCTION OF BOUNDARY STATES IN COSET CONFORMAL FIELD THEORIES"Nuclear Physics. B649. 205-242 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hiroshi Ishikawa: "BOUNDARY STATES IN COSET CONFORMAL FIELD THEORIES"Nuclear Physics. B629. 209-232 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 綿村 哲: "非可換"数学セミナー特集"21世紀のキーワード". 11. 34-37 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Maeda, S.Watamura: "Progress of theoretical physics, Supplement, Proceedings of the International Workshop on Noncommutative Geometry and String theory"Progress of theoretical physics, Kyoto. 201 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 綿村 哲: "超弦理論と数学の発展"数理科学. 462. 33-39 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Yoshiaki Maeda: "Noncommutative Differential Geometry and Its Application to Physics"Kluwer Academic Publishers. 306 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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