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The theory of oscillatory integral operator and its application to the Feynman path integral

Research Project

Project/Area Number 19540175
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ICHINOSE Wataru  Shinshu University, 理学部, 教授 (80144690)

Co-Investigator(Kenkyū-buntansha) 杉本 充  大阪大学, 理学研究科, 准教授 (60196756)
廣島 文生  九州大学, 数理学研究科, 准教授 (00330358)
熊ノ郷 直人  工学院大学, 工学部, 准教授 (40296778)
Co-Investigator(Renkei-kenkyūsha) HIROSHIMA Fumio  九州大学, 大学院・数理学研究院, 准教授 (00330358)
SUGIMOTO Mitsuru  大阪大学, 大学院・理学研究科, 准教授 (60196756)
KUMANOGO Naoto  工学院大学, 工学部, 准教授 (40296778)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
KeywordsFeynman経路積分 / 振動型積分作用素 / 擬微分作用素理論 / 量子力学 / スピン / 量子電磁気学 / Feyman経路積分 / 解の連続性 / 電磁場ポテンシャル / ローレンツゲージ / 汎関数微分 / 相関関数 / 電子電磁気学 / 光子の定常状態表現 / クーロンカの発生の数学的証明
Research Abstract

(1)電子など量子力学的粒子はスピンを持つことが知られている。スピンを込めた運動を記述するFeynman経路積分の厳密な定義を与え、これが従来から知られていた作用素論的な記述と一致することを示した。
(2)電子、陽子などの電荷を持った粒子は電磁場を介して相互作用する。電磁場を量子化して光子を取り扱い、これを媒介として荷電粒子が相互作用しているのを記述するのが量子電磁気学である。本研究では、量子電磁気学に対するFeynman経路積分の厳密な定義を与えることに成功した。

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (29 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 7 results) Presentation (16 results)

  • [Journal Article] On the Feynman path integral for nonrelativistic quantum electrodynamics2010

    • Author(s)
      一ノ瀬弥
    • Journal Title

      Rev. Math. Phys. 22,3

      Pages: 1-48

    • NAID

      120007114197

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Feynman path integral for nonrelativistic quantum electrodynamics2010

    • Author(s)
      W.Ichinose
    • Journal Title

      Review in Mathematical Physics 22(3)

      Pages: 1-48

    • NAID

      120007114197

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] L^2 stability and boundedness of the Fourier integral operators applied to the theory of the Feynman path integral2009

    • Author(s)
      一ノ瀬弥
    • Journal Title

      Proceeding of the 5th internatinal ISAAC Congress

      Pages: 423-428

    • Related Report
      2009 Final Research Report
  • [Journal Article] A mathematical remark on the Feynman path integral forthe quantum electro dynamics2009

    • Author(s)
      Wataru Ichinose
    • Journal Title

      Surikaisekiken kokyuroku (掲載決定済み) (in press)

    • Related Report
      2008 Annual Research Report
  • [Journal Article] A mathematical remark on the Feynman path integral for the quantum electrodynamics2008

    • Author(s)
      Wataru Ichinose
    • Journal Title

      Surikaisekiken Kokyurokuに発表(掲載決定済み)

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Phase space Feynman path integrals via piecewise bicharacteristic paths and their semiclassical approximations2008

    • Author(s)
      N. Kumano-go and D. Fujiwara
    • Journal Title

      Bulletin des Sciences Mathematiques(掲載決定済み, onlineで掲載済み)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical theory of the Feynman path integral for the generalized Pauli equations2007

    • Author(s)
      一ノ瀬弥
    • Journal Title

      J. Math. Soc. Japan vol. 59,3

      Pages: 649-668

    • NAID

      10019539892

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical note on the Feynman path integral for the quantum electrodynamics2007

    • Author(s)
      一ノ瀬弥
    • Journal Title

      Suurikaisekiken Kokyuuroku 1563

      Pages: 52-68

    • Related Report
      2009 Final Research Report
  • [Journal Article] A mathematical theory of the Feynman path integral for the generalized Pauli equations2007

    • Author(s)
      Wataru Ichinose
    • Journal Title

      J. Math. Soc. Japan 59

      Pages: 649-668

    • NAID

      10019539892

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The continuity of solutions with respect to a parameter to symmetric hyperbolic systems, Pseudo-Differential Operators: Analysis

    • Author(s)
      一ノ瀬弥
    • Journal Title

      Applications and Computation (に掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the continuity of solutions with respect to the electromagnetic potentials to the Schroedinger equations and the Dirac equations

    • Author(s)
      一ノ瀬弥
    • Journal Title

      Proceeding of the 7th internatinal ISAAC Congress (に掲載決定)

    • Related Report
      2009 Final Research Report
  • [Journal Article] The continuity of solutions with respect to a parameter to symmetric hyperbolic systems,

    • Author(s)
      W.Ichinose
    • Journal Title

      Pseudo-Differential Operators : Analysis, Applications and Computations (掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the continuity of solutions with respect to electromagnetic potentials to the Schroedinger and the Dirac equations

    • Author(s)
      W.Ichinose
    • Journal Title

      Proceeding of the 7^<th> international ISAAC Congress (掲載確定)

    • Related Report
      2009 Annual Research Report
  • [Presentation] On the continuity of the solutions with respect to coefficients to the Schroedinger equations and symmetric hyperbolic systems2010

    • Author(s)
      一ノ瀬弥
    • Organizer
      偏微分方程式松山キャンプ
    • Place of Presentation
      愛媛大学工学部
    • Year and Date
      2010-01-06
    • Related Report
      2009 Final Research Report
  • [Presentation] On the continuity of the solutions with respect to coefficients of the Schroedinger equations and symmetric hyperbolic systems2009

    • Author(s)
      一ノ瀬弥
    • Organizer
      第7回浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学工学部
    • Year and Date
      2009-12-22
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] On the continuity of the solutions with respect to the electromagnetic potentials to the Schroedinger2009

    • Author(s)
      一ノ瀬弥
    • Organizer
      the Dirac equations and the symmetric hyperbolic system equations, 作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-11-16
    • Related Report
      2009 Final Research Report
  • [Presentation] On the continuity of the solutions with respect to the electromagnetic potentials to the Schroedinger and the Dirac equations2009

    • Author(s)
      一ノ瀬弥
    • Organizer
      夏の作用素論セミナー
    • Place of Presentation
      盛岡
    • Year and Date
      2009-09-07
    • Related Report
      2009 Final Research Report
  • [Presentation] On the continuity of the solutions with respect to the electromagnetic potentials to the Schroedinger and the Dirac equations2009

    • Author(s)
      W.Ichinose
    • Organizer
      作用素論セミナー
    • Place of Presentation
      盛岡市民会館
    • Year and Date
      2009-09-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the continuity of the solutions with respect to the electromagnetic potentials to the Schroedinger and the Dirac equations2009

    • Author(s)
      一ノ瀬弥
    • Organizer
      ISAAC (The International Society Analysis, its Applications and Computation )
    • Place of Presentation
      Congress (London University, England)
    • Year and Date
      2009-07-14
    • Related Report
      2009 Final Research Report
  • [Presentation] On the continuity of the soulutions with respect to the electromagnetic potentials to the Schoedinger and the Dirac equations2009

    • Author(s)
      W.Ichinose
    • Organizer
      International Society Analysis, its Applications and Computation
    • Place of Presentation
      London University, England
    • Year and Date
      2009-07-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] シュレディンガー方程式の解の電磁場ポテンシャルに関する連続性2008

    • Author(s)
      一ノ瀬弥
    • Organizer
      谷口和夫教授還暦シンポジウム
    • Place of Presentation
      京都大学総合人間科学部
    • Year and Date
      2008-12-19
    • Related Report
      2009 Final Research Report
  • [Presentation] シュレデインガー方程式の解のポテンシャルに関する連続性2008

    • Author(s)
      Wataru Ichinose
    • Organizer
      谷口和夫還暦シンポジウム
    • Place of Presentation
      京都大学
    • Year and Date
      2008-12-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] QEDに関する経路積分の収束2008

    • Author(s)
      Wataru Ichinose
    • Organizer
      夏の作用素論研究会
    • Place of Presentation
      佐賀市
    • Year and Date
      2008-09-07
    • Related Report
      2008 Annual Research Report
  • [Presentation] The stability of the oscillatory integral operators applied to the Feynman path integral and problems for it2008

    • Author(s)
      Wataru Ichinose
    • Organizer
      The international conference "Function spaces in the differential equations"
    • Place of Presentation
      大阪大学
    • Year and Date
      2008-02-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] QEDに関する経路積分の収束について2008

    • Author(s)
      一ノ瀬弥
    • Organizer
      夏の作用素論セミナー
    • Place of Presentation
      佐賀市
    • Related Report
      2009 Final Research Report
  • [Presentation] The stability of the oscillatory integral operators applied to the Feynman path integral and problems for it2008

    • Author(s)
      一ノ瀬弥
    • Organizer
      The international conference ''Function spaces in the differential equations''
    • Place of Presentation
      Osaka University
    • Related Report
      2009 Final Research Report
  • [Presentation] 非有界な関数のリーマン和の収束定理2007

    • Author(s)
      Wataru Ichinose
    • Organizer
      14回「超局所解析と古典解析」
    • Place of Presentation
      和歌山市
    • Year and Date
      2007-12-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非有界な関数のリーマン和の収束定理2007

    • Author(s)
      一ノ瀬弥
    • Organizer
      研究集会第14回「超局所解析と古典解析」
    • Place of Presentation
      和歌山市
    • Related Report
      2009 Final Research Report
  • [Presentation] Some mathematical remarks on the Feynman path integral for the nonrelativistic quantum electrodynamics2007

    • Author(s)
      一ノ瀬弥
    • Organizer
      10th Quantum Mathematics International Conference
    • Place of Presentation
      Moeciu, Roomania
    • Related Report
      2009 Final Research Report 2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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