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Algebro-analytic study of quantum integrable systems

Research Project

Project/Area Number 20340027
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionRikkyo University

Principal Investigator

JIMBO Michio  Rikkyo University, 理学部, 教授 (80109082)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000)
Fiscal Year 2010: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2009: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2008: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
KeywordsXXZ模型 / 可積分場の理論 / 共形場理論 / 相関関数 / 量子アフィン代数フェルミオン / sine-Gordon模型 / フェルミオン / gl(∞) / 量子戸田方程式 / Whittakerベクトル
Research Abstract

In the space of local operators of quantum integrable systems, we have introduced a new fermionic basis and described their expectation values. More specifically, in the 6 vertex model we defined an action of fermions on quasi-local operators, and in a very general setting expressed their expectation values of the fermionic basis in terms of a single function of two variables. In the limit to conformal field theory we determined the relation between the fermionic and Virasoro bases for low degrees. We also proposed a novel framework for calculating the one point functions in the sine-Gordon model.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (25 results)

All 2011 2010 2009 2008 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results) Presentation (10 results)

  • [Journal Article] Hidden Grassmann structure in the XXZ model V : sine-Gordon model2011

    • Author(s)
      M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      Lett.Math.Phys. 96巻

      Pages: 325-365

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model V : Sine-Gordon model2011

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      To appear in Lett.Math.Phys.

      Volume: 96 Pages: 325-365

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] One-point function of descendants in sine-Gordon model2010

    • Author(s)
      M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      Proceedings of the workshop 'New Trends in Quantum Integrable Systems'(Eds.B.Feigin, M.Jimbo, M.Okado)(World Scientific)

      Pages: 117-137

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model IV : CFT limit2010

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      Commun.Math.Phys. 299巻

      Pages: 825-866

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On one-point functions of descendants in sine-Gordon model2010

    • Author(s)
      M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      "New Trends in Quantum Integrable Systems : Proceedings of the Infinite Analysis 09", World Scientific Publishing, Singapore

      Pages: 117-137

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model IV : CFT limit2010

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      Commun.Math.Phys.

      Volume: 299 Pages: 825-866

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian2009

    • Author(s)
      B.Feigin, E.Feigin, M.Jimbo, T.Miwa, E.Mukhin
    • Journal Title

      Lett.in Math.Phys. 88巻

      Pages: 39-77

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Completeness of a fermionic basis in the homogeneous XXZ model2009

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      J.Math.Phys. 50巻(online)

      Pages: 95206-95206

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model III : Introducing Matsubara direction2009

    • Author(s)
      M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      J.Phys.A : Math.Theor. 42巻

      Pages: 304018-304018

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model II : Creation operators2009

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov, Y.Takeyama
    • Journal Title

      Commun.Math.Phys. 286巻

      Pages: 875-932

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model III : Introducing Matsubara direction2009

    • Author(s)
      M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      J.Phys.A : Math.Theor. 42

    • Related Report
      2009 Annual Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian2009

    • Author(s)
      B.Feigin, E.Feigin, M.Jimbo, T.Miwa, E.Mukhin
    • Journal Title

      Lett.in Math.Phys. 88

      Pages: 39-77

    • Related Report
      2009 Annual Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Completeness of a fermionic basis in the homogeneous XXZ model2009

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      J.Math.Phys. 50

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Completeness of a fermionic basis in the homogeneous XXZ model2009

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      Journal of Mathematical Physics 50

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hidden Grassmann structure in the XXZ model IV : CFT limit

    • Author(s)
      H.Boos, M.Jimbo, T.Miwa, F.Smirnov
    • Journal Title

      To appear in Commun.Math.Phys. (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] サイン ゴルドンモデルの可積分構造をめぐって2011

    • Author(s)
      神保道夫
    • Organizer
      場の理論・量子重力研究会
    • Place of Presentation
      立教大学
    • Year and Date
      2011-01-06
    • Related Report
      2010 Final Research Report
  • [Presentation] サイン ゴルドンモデルにおけるフェルミオン構造2010

    • Author(s)
      神保道夫
    • Organizer
      日本数学会秋期総合分科会
    • Place of Presentation
      名古屋大学(特別講演)
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] What are the 'full symmetries' in quantum integrable models?2010

    • Author(s)
      神保道夫
    • Organizer
      Group Theoretical Methods in Physics 2010
    • Place of Presentation
      Newcastle(招待講演)
    • Year and Date
      2010-07-28
    • Related Report
      2010 Final Research Report
  • [Presentation] What are the 'full symmetries' in quantum integrable models?2010

    • Author(s)
      Michio Jimbo
    • Organizer
      Group Theoretical Methods in Physics 2010
    • Place of Presentation
      Newcastle, UK
    • Year and Date
      2010-07-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] One-point functions in the sine-Gordon model2010

    • Author(s)
      神保道夫
    • Organizer
      Recent Advances in Quantum Integrable Systems 2010
    • Place of Presentation
      Annecy, France(招待講演)
    • Year and Date
      2010-06-16
    • Related Report
      2010 Final Research Report
  • [Presentation] One-point functions in the sine-Gordon model2010

    • Author(s)
      Michio Jimbo
    • Organizer
      Recent Advances in Quantum Integrable Systems 2010
    • Place of Presentation
      Annecy, France
    • Year and Date
      2010-06-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Hidden Grassmann structure in the XXZ model2009

    • Author(s)
      神保道夫
    • Organizer
      Tokyo-Seoul Conference in Representation Theory
    • Place of Presentation
      東京大学数理科学研究科(招待講演)
    • Year and Date
      2009-12-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Hidden Grassmann structure in the XXZ model2009

    • Author(s)
      Michio Jimbo
    • Organizer
      Tokyo-Seoul Conference on Representation Theory
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2009-12-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Hidden fermionic structure in the XXZ model II : Technical details2008

    • Author(s)
      神保道夫
    • Organizer
      Workshop 'Quantum integrable systems and solvable statistical mechanical models'
    • Place of Presentation
      CRM, Montreal(招待講演)
    • Related Report
      2010 Final Research Report
  • [Presentation] A fermionic structure in the XXZ model2008

    • Author(s)
      神保道夫
    • Organizer
      Workshop 'From Painleve to Okamoto'
    • Place of Presentation
      東京大学数理科学研究科(招待講演)
    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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