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Quantum Theory of Totally Constrained Systems and its Application to Gravity Theories

Research Project

Project/Area Number 08640370
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
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) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1998: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
Keywordsgeneral relativity / quantum gravity / canonical theory / totally constrained systems / black hole / thermodynamics / gauge-invariant perturbation theory / ブラックホール熱力学 / 振動論 / 局所一様時空 / 摂動論
Research Abstract

The main results obtained by the research from 1996 through 1998 are summarized as follows :
1) Canonical structure of locally homogeneous systems : For a locally homogeneous system on a compact 3-dimensional space, a general algorithm to determine the canonical structure of the phase space consisting of all diffeomorphism classes of initial data sets was developed, and the moduli degrees of freedom were shown to be constants of motion. Further, with the help of the algorithm, the canonical structures of pure gravity systems of the Thurston type E3, Nil and Sol were completely classified to show that the canonical structure often becomes degenerate in the moduli sector.
2) Quantum Bianchi model : On the basis of the result in I), the quantum dynamics of the type E3 systems with compact space was analyzed in terms of the new formalism (Web formalism) proposed by the head investigator and was compared with the treatment in terms of the conventional Wheeler-DeWitt equation. The most importa … More nt result is the discovery of the fact that the quantum dynamics in the Web formalism is described not by solutions to the Wheeler-DeWitt equation but rather by their extensions in the distribution sense in general.
3) Perturbation of scalar fields on an expanding universe : the structure of the gauge-invariant perturbation theory was investigated in detail for the system consisting of scalar fields and gravity on a spatially homogeneous and isotropic expanding universe background. It was found that there is a general correspondence between the long-wavelength limit of gauge-invariant perturbations and the homogeneous perturbations of the homogeneous background solution. Further, with the help of this correspondence, the evolutions of superhorizon scale perturbations in the reheating stage of inflationary models were investigated analytically to establish the conservation law of the Bardeen parameter during this stage.
4) Black hole thermodynamics : On the basis of the idea of entanglement, thermodynamics was constructed for a quantum scalar field on the flat spacetime and on black hole spacetimes. It was shown that the entanglement thermodynamics thus constructed for the black hole spacetimes has the same structure as that of the classical black hole thermodynamics. Less

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] Kodama H.and Hamazaki T.: "Evolution of cosmological perturbations in a stage dominated by an oscillatory scalartiels" Prog. Theor Phys.96. 949-970 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hamazaki T.and Kodama H.: "Evolution of cosmological perturbations during veheating" Prog. Theor Phys.96. 1123-1145 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hukouyama S., Seriu M.and Kodama H.: "Can the entanslement entrogy be the origin of black-hole entropy?" Phys.Rev.D55. 7666-7679 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kodama H.: "Canonical Structure of Locally Honogeneous Systems on Compart Closed 3-Hanifolds of Tyre E^3, Nil and sol" Prog.Theor.Phys.99. 173-236 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kodama H.and Hamazaki T.: "Evolution of Cosmological Perturbarions on the Long Wave Length Limit" Phys.Rev.D57. 7177-7185 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Mukohyama S., Serin M. and Kodama H.: "Ther mo dynamics of entanslement in Schwarzschild Spacetime" Phys. Rev.D58. 064001 : 1-11 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 小玉 英雄: "相対性理論" 培風館, 309 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 小玉 英雄: "磯辺他編「天文学ハンドブック」第1章第2節宇宙の初期進化" 朝倉書店(印刷中), (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kodama H.and Hamazaki T.: "Evolution of cosmo-logical perturbations in a stage dominated by an os-cillatory scalar field" Prog.Theor.Phys. 96. 949-970 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hamazaki T.and Kodama H.: "Evolution of cosmo-logical perturbations during reheating" Prog.Theor.Phys. 96. 1123-1145 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Mukouyama S., Seriu M.and Kodama H.: "Can the entanglement entropy be the origin of black-hole en-tropy?" Phys.Rev.D55. 7666-7679 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kodama H.: "Canonical Structure of Locally Homo-geneous Systems on Compact Closed 3-Manifolds of Type E^3, Nil and Sol" Prog.Theor.Phys. 99. 173-236 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kodama H.and Hamazaki T.: "Evolution of Cosmo-logical Perturbations in the Long Wavelength Limit" Phys.Rev.D57. 7177-7185 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Mukohyama S., Seriu M.and Kodama H.: "Thermody-namics of entanglement in Schwarzshild spacetime" Phys.Rev.D58. 064001 : 1-11 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Hideo Kodama: "Canonical Stracture of Locally Homogeneous Systems on Compaut Closed 3-Manifolds of Type E^3,N:I and Sal" Prog.Theor.Phys.99. 173-236 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Kodama and T.Hamazaki: "Evolution of Cosmological Perturbations on the Long Wave lensth Limit" Phys.Rev.D. 57. 7177-7185 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Mukohyama,M.Serin and H.Kodama: "Thermodynamics of entenglemint in Schusrzschild spacetima" Phys.Rev.D. 58. 064001:1-11 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] S.Mukouyama, M.Seriuma H.Kodama: "Can the entanglement entropy be the origin of black-hole entropy" Physical Review. D55. 7666-7679 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kodama: "Can onical Structure of Locally Homogeneous Systems on Compact Closed 3-Manifolds of Type E^3,N:1 and Sol" Progress of Theoretical Physics. 99. 173-236 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 小玉英雄: "相対性理論" 培風館, 309 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Kodama and T.Hamazaki: "Evolution of cosmological perturbations in a stage dominated by an osillatory scalar field" Prog.Theor.Phys.96巻5号. 949-970 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Hmazaki and H.Kodama: "Evolution of cosmological perturbations during reheating" Prog.Theor.Phys.96巻6号. 1123-1145 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 小玉英雄: "相対性理論" 培風館, 310 (1997)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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