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Structure of observables and dynamics in 4-dimonsional canonical quantum grarit

Research Project

Project/Area Number 05640340
Research Category

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

Allocation TypeSingle-year Grants
Research Field 素粒子・核・宇宙線
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

KODAMA Hideo  Kyoto University, Yukawa Institute for Theoretical Physics, Professor, 基礎物理学研究所, 教授 (40161947)

Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1995: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1994: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1993: ¥700,000 (Direct Cost: ¥700,000)
Keywordsgeneral relativity / quantum gravity / canonical quantization / constrained system / von Neumann algebra / 相対性理論 / 正準理論 / 量子重力 / 完全拘束系 / モジュライ空間 / 微分幾何学
Research Abstract

In this research we constructed a new formulation of quantum theory of totally constrained systems in order to resolve one of the main difficulties concerning the treatment of time variables and dynamics in 4-dimensional canonical quantum gravity. In this formulation quantum constraints are imposed on a relative amplitude functional on an unconstrained state space unlike the conventional Dirac procedure in which the constraints are imposed on state vectors themselves to pick up physical states. This modification enables us to include time variables into observables, and to describe dynamics as mappings among acausal subspaces in the unconstrained state space. One important achievement of our research is the proof of the consistency of dynamics in this formalism. The main idea is to utilize special subalgebras of the von Neumann algebra consisting of constants of motion obtained by its central decomposition to pick up a special family of acausal subspaces called IPASs. We have shown rigorously that dynamical mappings among IPASs are conformal if the von Neumann algebra of constants of motion is of type I,which guarantees the consistency. Further, by applying this formalism to systems wich a single constraint, which include minisuperspace models, we have shown that their dynamics have the same structure as those of ordinary quantum mechanical systems without constraints.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Yoshihisa Fujiwara: "Comments on closed Bianchi models" Class. Quantum Gravity. 10. 859-868 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hideo Kodama: "Does a domain wall omit gravitational wars?" Phys. Rev. D. 50. 7292-7303 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Yutaka Fujita: "Influence of cooling flow and galactic motion on the iron distribution in clustrrs of galaxies" Astrophys. J.452. 177-188 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hideo Kodama: "Pynamics of Totally Constrained Systems I. Classical Theory" Prog. Theor. Phys.94. 475-501 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hideo Kodama: "Dynamics of Totally Constrained Systems II. Quantum Theory" Prog. Theor. Phys.94. 937-987 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Takashi Hamazaki: "Evolution of Cosmological Perturbations during Reheating" Proc. 3rd. workshop on General Relativity. 1(発表予定). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 小玉英雄: "量子情報と進化の力学(大矢雅則,小嶋泉 編)第3章" 牧野書店, 15 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 小玉英雄: "相対性理論" 培風館(印刷中), 250 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Fujiwara, H.Ishihara, and H.Kodama: "Comments on closed Bianchi models" Class.Quantum Gravity. 10. 859-868 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kodama, H.Ishihara and Y.Fujiwara: "Does a domain wall emit gravitational waves? - Gauge-invariant perturbative treatment" Phys.Rev.D. 50. 7292-7303 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Fujita and H.Kodama: "Influence of cooling flow and galactic motion on the iron distribution in clusters of galaxies" Astrophys. J.452. 177-188 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kodama: "Dynamics of Totally Constrained Systems I.Classical Theory" Prog.Theor.Phys.94. 475-501 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kodama: "Dynamics of Totally Constrained Systems II.Quantum Theory" Prog.Theor.Phys.94. 937-987 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Hamazaki and H.Kodama: "Evolution of Cosmological Perturbations during Reheating" Proc.3rd Workshop on General Relativity and Gravity. (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kodama: Necessity and Accidentalness in Evolutionary Cosmology. in Quantum Information and Dynamics of Evolution, ed.M.Ooya and I.Ojima, Chapter 3 (Makino Shoten), (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Kodama: Theory of Relativity. Baihukan (in press), 250 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hideo Kodama: "Dynamics of Totally Constrained Systems I. Classical Theory" Prog. Theor. Phys.94. 471-501 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hideo Kodama: "Dynamics of Totally Constrained Systems II. Quantum Theory" Prog. Theor. Phys.94. 937-987 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小玉英雄: "量子情報と進化の力学(大矢雅則,小嶋泉編)(第3章)" 牧野書店, 15 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 小玉英雄: "相対性理論" 培風館(印刷中), 250 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hideo Kodama,Hideb:Ishihara,Yosb:h:sa Fajimarn: "Does a domain wall emit gravitatioral waves?" Dhys.Rev.D. 50. 7292-7303 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Hideo Kodama: "Quantum Gravity by the Complex Canonical Formulation" Int.J.Mod.Phys.D. 1. 439-523 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Yoshihisa Fujiwara: "Comments on closed Bianchi models" Class.Quantum Gravity. 10. 859-868 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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