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Mathematical problems in quantum field theory and infinite dimensional analysis

Research Project

Project/Area Number 15K04888
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionHokkaido University

Principal Investigator

Arai Asao  北海道大学, 理学研究院, 特任教授 (80134807)

Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsフォック空間 / 無限次元解析 / 無限次元デイラック作用素 / 無限次元ラプラシアン / 超対称性 / 超対称的量子場 / 時間作用素 / 正準交換関係と正準反交換関係の表現 / 量子場 / 正準反交換関係 / 基底状態 / 正準交換関係 / 量子ディラック場 / 無限次元ディラック作用素 / 縮退度 / ハミルトニアン / ディラック場 / スカラー場
Outline of Final Research Achievements

(1) An upper bound for the multiplicity of ground state of a class of quantum field models has been derived. (2) Detailed analyses have been done on in-equivalent representations of canonical commutation relations and canonical anti-commutation relations, which have physically important meanings. (3) For a general quantum system, a concept of ultra-weak time-operator has been introduced. Hierarchies of time-operators and their respective physical roles have been considered.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (13 results)

All 2018 2017 2016 2015

All Journal Article (6 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 4 results,  Open Access: 1 results) Presentation (5 results) (of which Int'l Joint Research: 4 results,  Invited: 5 results) Book (2 results)

  • [Journal Article] Ultra-Weak Time Operators of Schroedinger Operators2017

    • Author(s)
      Asao Arai and Fumio Hiroshima
    • Journal Title

      Annales Henri Poincare

      Volume: 16 Issue: 9 Pages: 2995-3033

    • DOI

      10.1007/s00023-017-0586-x

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 量子場の数理解析2017

    • Author(s)
      新井朝雄
    • Journal Title

      数学

      Volume: 69 Pages: 255-279

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ultra-weak time operators of Schroedinger operators2017

    • Author(s)
      Asao Arai, Fumio Hiroshima
    • Journal Title

      Annales Henri Poincare

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Inequivalence of quantum Dirac fields of different masses and the underlying general structures involved2017

    • Author(s)
      Asao Arai
    • Journal Title

      EMS Series of Congress Reports: Functional Analysis and Operator Theory for Quantum Physics

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Upper bounds on the degeneracy of the ground state in quantum field models2016

    • Author(s)
      Asao Arai, Daiju Funakawa
    • Journal Title

      Advances in Mathematical Physics

      Volume: 2016 Pages: 1-13

    • DOI

      10.1155/2016/8908413

    • NAID

      120005712480

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Golden-Thompson type inequalities and functional integral approach to boson-fermion system2015

    • Author(s)
      Asao Arai
    • Journal Title

      RIMS Kokyuroku

      Volume: 1975 Pages: 24-31

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Presentation] Inequivalence of quantum Dirac fields of different masses and general structures behind it2017

    • Author(s)
      Asao Arai
    • Organizer
      Physical and mathematical approaches to interacting particle systems---In honor of 70th birthday of Herbert Spohn, Tokyo Institute of Technology
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Spectral analysis of infinite dimensional Dirac operators on an abstract boson-fermion Fock space2017

    • Author(s)
      Asao Arai
    • Organizer
      RIMS研究会「量子場の数理とその周辺 2017」,京都大学数理解析研究所
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Inequivalence of quantum Dirac fields of different masses and general structures behind it2017

    • Author(s)
      Asao Arai
    • Organizer
      Physical and mathematical approaches to interacting particle systems---In honor of 70th birthday of Herbert Spohn
    • Place of Presentation
      東京都目黒区 東京工業大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Inequivalence of quantum Dirac fields of different masses and a general structure behind it2016

    • Author(s)
      Asao Arai
    • Organizer
      Mathematical quantum field theory and related topics
    • Place of Presentation
      福岡県福岡市 九州大学IMI
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Inequivalent Weyl representations of canonical commutation relations in an abstract Bose field theory2015

    • Author(s)
      Asao Arai
    • Organizer
      RIMS研究集会「量子場の数理とその周辺 2015」
    • Place of Presentation
      京都大学数理解析研究所,京都府京都市
    • Year and Date
      2015-10-07
    • Related Report
      2015 Research-status Report
    • Invited
  • [Book] Analysis on Fock Spaces and Mathematical Theory of Quantum Fields2018

    • Author(s)
      Asao Arai
    • Total Pages
      862
    • Publisher
      World Scientific
    • ISBN
      9789813207110
    • Related Report
      2017 Annual Research Report
  • [Book] Functional Analysis and Operator Theory for Quantum Physics2017

    • Author(s)
      Asao Arai 他 分担執筆 (J. Dittrich 他編集)
    • Total Pages
      597
    • Publisher
      European Mathematical Society
    • ISBN
      9783037191750
    • Related Report
      2017 Annual Research Report

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Published: 2015-04-16   Modified: 2019-03-29  

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