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The theory of unbounded derivations in C^*-algebras and its applications to Statistical mechanics.

Research Project

Project/Area Number 61540132
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNihon University

Principal Investigator

SAKAI Shoichiro  College of Humanities and Sciences, Nihon university, 文理学部, 教授 (30130503)

Co-Investigator(Kenkyū-buntansha) SUZUKI Masahiko  College of Humanities and Sciences, Nihon university, 文理学部, 講師 (00171249)
SUZUKI Osamu  College of Humanities and Sciences, Nihon university, 文理学部, 助教授 (10096844)
GOTO Shiro  College of Humanities and Sciences, Nihon university, 文理学部, 教授 (50060091)
MISONOU Yoshinao  College of Humanities and Sciences, Nihon university, 文理学部, 教授 (20005705)
NIIRO Fumio  College of Humanities and Sciences, Nihon university, 文理学部, 教授 (50012191)
石原 繁  日本大学, 文理学部, 教授 (80016013)
Project Period (FY) 1986 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1986: ¥900,000 (Direct Cost: ¥900,000)
KeywordsContinuous quantum systems / C^*-quantum physics / Derivation / 平衝状態 / C^*ー力学系 / 非有界微分 / 【C^*】-代数 / 統計力学 / 相転移 / 【C^*】-力学系
Research Abstract

The study of the axiomatization of continuous quantum systems within the framework of C^*-algebras or more general ^*-algebras has been done, we have obtained various sufficient condions in order that there exist time evolutions and K M S states in the systems.

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1986 Annual Research Report
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] 境正一郎: Contemporary Mathematics,A.M.S.62. 187-217 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 境正一郎: Contemporary Mathematics,A.M.S.62. 413-426 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 境正一郎: 数理解析研究所構究録. 651. 132-143 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "Perturbations and K M S states in C^*-dynamical systems (Generalization of the absence theorem of phase transition to continuous quantum systems)" Contemporary Mathematics, A.M.S.62. 187-217 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "Dynamics in continuous quantum systems" Contemporary Mathematics, A.M.S.62. 413-426 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "On Stone - Weierstrass theorem for C^*- algebras" Lecture notes, R I M S. 651. 132-143 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] Shoichiro Sakai: Operator algebras in Dynamical syotems (the theory of unbounded derivations in C^*- algebras). Cambridge university press, 300 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] 境正一郎: 京都大学数理解析研究所講究録.

    • Related Report
      1988 Annual Research Report
  • [Publications] 境正一郎: "Operator algebras in dynamical systems" Cambridge University Press, 180 (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] 境正一郎: Contemporary Mathematics,American Mathematical Society. 62. 187-217 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] 境正一郎: Contemporary Mathematics,American Mathematical Society. 62. 413-426 (1987)

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-31   Modified: 2016-04-21  

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