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Clarification of the phase space structure of the tropical integrable systems

Research Project

Project/Area Number 25400122
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research Institution防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)

Principal Investigator

Takagi Taichiro  防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 応用科学群, 教授 (00531766)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords可積分系 / 組合せ論 / 離散戸田格子 / トロピカル幾何学 / ソリトン / ベーテ仮説 / 共形場理論 / 演算子積展開 / 積分表示 / ヤング図形 / 超離散化 / 戸田格子 / ラックス形式
Outline of Final Research Achievements

We clarified several properties of the phase space structures of the tropical periodic Toda lattice. This model is defined as a tropical limit of the discrete periodic Toda lattice, a variation of the Toda lattice which is one of the most famous models in the field of classical integrable systems. Especially, we proved that the Young diagrams defined through the Lax representation of the discrete periodic Toda lattice coincide with the Young diagrams defined as continuous limits of the corresponding diagrams defined in the combinatorial theory of the Bethe ansatz of the quantum spin chains. In addition, during a process of widening the author’s vision to find a breakthrough in future studies, we considered somehow different kind of problems in the field of integrable systems and found a new result on generalized Wick theorems in conformal field theory.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (10 results)

All 2017 2016 2015 2014 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (8 results) (of which Int'l Joint Research: 2 results)

  • [Journal Article] A New Generalized Wick Theorem in Conformal Field Theory2017

    • Author(s)
      Taichiro Takagi
    • Journal Title

      Theoretical and Mathematical Physics

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice2014

    • Author(s)
      Taichiro Takagi
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 47 Issue: 39 Pages: 395201-395201

    • DOI

      10.1088/1751-8113/47/39/395201

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 共形場理論における一般化されたWickの定理と Borcherds恒等式2017

    • Author(s)
      高木 太一郎
    • Organizer
      日本物理学会第72回年次大会
    • Place of Presentation
      大阪府,豊中市
    • Related Report
      2016 Annual Research Report
  • [Presentation] Generalized Wick theorems in conformal field theory and the Borcherds identity2016

    • Author(s)
      Taichiro Takagi
    • Organizer
      Workshop on Classical and Quantum Integrable Systems
    • Place of Presentation
      Euler International Mathematical Institute, Saint-Petersburg, Russia
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 共形場理論における一般化されたWickの定理と Borcherds恒等式2016

    • Author(s)
      高木 太一郎, 吉川 拓真
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪府,吹田市
    • Related Report
      2016 Annual Research Report
  • [Presentation] Young diagrams associated with the tropical periodic Toda lattice2015

    • Author(s)
      Taichiro Takagi
    • Organizer
      Nonlinear Evolution Equations and Dynamical Systems 2015
    • Place of Presentation
      Hotel Flamingo, S. Margherita di Pula, Sardinia, Italy
    • Year and Date
      2015-05-27
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] トロピカル周期戸田格子と Kerov-Kirillov-Reshetikhin 全単射2015

    • Author(s)
      高木 太一郎
    • Organizer
      日本数学会2015年会
    • Place of Presentation
      明治大学駿河台キャンパス(東京都)
    • Year and Date
      2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Commuting phase flows in the tropical periodic Toda lattice

    • Author(s)
      Taichiro Takagi
    • Organizer
      Conference on Nonlinear Mathematical Physics: Twenty Years of JNMP
    • Place of Presentation
      ソフス・リー会議センター, ノルフィヨーレイド, ノルウェー王国
    • Related Report
      2013 Research-status Report
  • [Presentation] Commuting Phase Flows in the Tropical Periodic Toda Lattice

    • Author(s)
      Taichiro Takagi
    • Organizer
      XXV IUPAP International Conference on Statistical Physics
    • Place of Presentation
      ソウル国立大学, ソウル, 大韓民国
    • Related Report
      2013 Research-status Report
  • [Presentation] トロピカル周期戸田格子の保存量とその最近接排他表現

    • Author(s)
      高木 太一郎
    • Organizer
      日本物理学会第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス(神奈川県)
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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