Quantum Theory of Totally Constrained Systems and its Application to Gravity Theories
Project/Area Number  08640370 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
素粒子・核・宇宙線

Research Institution  KYOTO 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 Fiscal Year 
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)

Keywords  general relativity / quantum gravity / canonical theory / totally constrained systems / black hole / thermodynamics / gaugeinvariant perturbation theory / 一般相対論 / 量子重力 / 正準理論 / 完全拘束系 / ブラックホール / 熱力学 / ゲージ不変摂動論 / 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 3dimensional 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 WheelerDeWitt 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 WheelerDeWitt 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 gaugeinvariant 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 longwavelength limit of gaugeinvariant 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
(5results)
Research Output
(23results)