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Macroscopic Variables and Hilbert C^*-Modules in Algebraic Quantum Field Theory

Research Project

Project/Area Number 11640113
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

OJIMA Izumi  Kyoto University., RIMS, Assoc. Prof., 数理解析研究所, 助教授 (60150322)

Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsSpontaneous symmetry breaking / Tannaka-Krein duality / Algebraic quantum field theory / C^*-category / Homotopy / Induced representations / Superselction theory / Order parameters / 超対称性 / de Rhamカレント / 超伝導 / Josephson効果 / 対称性の破れ
Research Abstract

In 1999 together with Prof. Maumary (Univ. de Lausanne, Switzerland) I clarified deep connections between supersymmetry and homotopy formulated in an algebraic and categorical form (S.Maumary and I.Ojima, "Supersymmetry and Homotopy" which is now under revision). Along the general formulation of macroscopic variables arising from spontaneous symmetry breaking (SSB), I investigated the Josephson effect as the most important ingredient in superconductivity : In contrast to the traditional derivation whose general validity is unclear, I succeeded in obtaining a concise derivation of the Josephson formulae which clarifies the essence of Josephson current as the physical effect due to the difference in order parameters accross two adjacent phases. In close connection with this theme, I have continued the research on the general formulation of local temperature states in algebraic QFT together with Profs.D.Buchholz, H.Roos in Germany (to be completed by the coming summer) and on the generali … More zation of superselction theory to SSB cases the latter of which constitutes the main contents of my research in 2000.
Regarding the later, I have worked on mathematical preparations for it : In contrast to Tannaka-Krein duality for compact groups playing the essential roles in the cases of unbroken symmetry, the extension of duality to homogeneous spaces becomes important in our case of SSB.What I obtained with Prof. Maumary is a result for this extension in use of the homotopy-fiber category, on the basis of which the research has been going on. To completie the project, we need to combine this result with a method which allows the extension of the algebra with unbroken subgroup symmetry to a larger one with full symmetry. For this purpose, the investigation on Goldstone multiplets, order parameters and the centres of represented algebras done in preparation for my series lectures "Thermal Instability of Supersymmetry I, II") at Borel Seminar 2000 is expected to play important roles. Along these lines, the project is expected to be completed this year. Less

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] Izumi Ojima: "Spontaneous Collapse of Supersymmetry"in Proceedings of the 2nd Jagna International Workshop"Mathematical Methods of Quantum Physics"(Gordon and Breach). 275-286 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "Symmetry Breaking Patterns-Spontaneous Collapse of SUSY and Others-"in"Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability",eds.L.Accardi,H.-H.Kuo,N.Obata,K.Saito,Si Si and L.Streit,(Italian School of East Asian Studies). 337-353 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 小嶋泉: "Towards Local Temperature States in QFT"京大数理研講究録「量子情報と量子カオスの数理」. 1142. 123-136 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"Lett.Math.Phys.. 51. 257-264 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "Spontaneous Collapse of supersymmetry"in Proc. 2nd Jagna Intern. Workshop on "Mathematical Methods of Quantum Physics" eds. C.C.Bernido, et al., (Gordon Breach). 275-286 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "Symmetry Breaking Patters-Spontaneous Collapse of SUSY and Others-""Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability", eds. L.Accardi, H.-H.Kuo, N.Obata, K.Saito, Si Si and L.Streit, (Italian School of East Asian Studies). 337-353 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "Towards Local Temperature States in QFT"RIMS Kokyuroku "Mathematical Aspects of Quantum Information and Quantum Chaos". No. 1142. 123-136 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"Lett. Math. Phys.. 51. 257-264 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Ojima: "Symmetry Breaking Patterns-Spontaneous Collapse of SUSY and Others-"in "Trends in Contemporary Infinite Dimensional Analysis and Quantum Probability", eds.L.Accardi,H.-H.Kuo, N.Obata, K.Saito, Si Si and L.Streit, (Italian School of East Asian Studies). 337-353 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 小嶋泉: "Towards Local Temperature States in QFT"京大数理研講究録「量子情報と量子カオスの数理」. 1142. 123-136 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"Lett.Math.Phys.. 51. 257-264 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Izumi Ojima: "Spontaneous Collapse of Supersymmetry"in Proceedings of the 2nd Jagna International Workshop "Mathematical Methods of Quantum Physics" (Gorden and Breach). 275-286 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Izumi Ojima: "Symmetry Breaking Patterns -Spontaneous Collapse of SUSY and Others-"to appear in "Classical and Quantum White Noise", eds.L.Accardi,H.-H.Kuo,L.Streit,Si Si and K.Saito (Kluwer Publ.Co.). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] 小嶋 泉: "Towards Local Temperature States in QFT"to appear in 京大数理研講究録「量子情報と量子カオスの数理」. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Izumi Ojima: "A Simple Derivation of Josephson Formulae in Superconductivity"to appear in Lett.Math.Phys.. (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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