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

全约束系统的量子理论及其在引力理论中的应用

基本信息

批准号：
08640370
负责人：
KODAMA Hideo
金额：
$ 1.34万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

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

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 modulo degrees of freedom were shown to be constants of motion.此外，借助算法，瑟斯顿E3型纯重力系统的规范结构完全分类，以表明规范结构通常在模量扇区中退化。2）量子比安奇模型。由主管调查员与常规Wheeler-Dewitt方程式进行了比较。最重要的……更重要的结果是发现了一个事实，即网络形式中的量子动态不是通过对Wheeler-Dewitt方程的解决方案来描述的，而是通过将其扩展在分布意义上的扩展来描述。3）标量在扩展的宇宙上的标量扰动：扩展的范围：量表的结构在量表上呈现量的结构，并在范围内调查了量表的范围，并在详细范围内调查了量表的范围，并在详细范围内构成了量表的范围，并在范围内逐渐研究。各向同性扩展宇宙背景。发现量规不变的扰动的长波长极限与均匀背景解决方案的均匀扰动之间存在一般对应关系。此外，在分析上研究了通货膨胀模型的再加热阶段，超级尺度尺度扰动的发展，以在此阶段建立Bardeen参数的保护定律。4）黑洞热力学。结果表明，因此为黑洞空位构建的纠缠热力学具有与经典黑洞热力学的结构相同的结构。较少的