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

1996年至1998年的研究取得的主要成果概括如下：1）局部齐次系统的规范结构：对于紧3维空间上的局部齐次系统，确定相空间规范结构的通用算法开发了由初始数据集的所有微分同胚类组成的模型，并且自由模度被证明是运动常数。此外，借助该算法，纯重力系统的规范结构。 Thurston E3 型系统的 Nil 和 Sol 被完全分类，以表明规范结构经常在模部分变得简并。2) 量子 Bianchi 模型：在 I) 的结果的基础上，E3 型系统的量子动力学根据首席研究员提出的新形式主义（Web 形式主义）对具有紧凑空间的处理进行了分析，并与 Wheeler-DeWitt 常规方程的处理进行了比较。最重要的结果是发现事实上，网络形式主义中的量子动力学不是通过惠勒-德威特方程的解来描述的，而是通过它们在一般分布意义上的扩展来描述的。3) 膨胀宇宙上标量场的扰动：规范的结构对空间均匀、各向同性膨胀宇宙背景下的标量场和引力系统的不变摄动理论进行了详细研究，发现规范不变的长波长极限之间存在一般对应关系。进一步，借助该对应关系，分析研究了暴胀模型再加热阶段超地平线尺度扰动的演化，建立了该阶段巴丁参数的守恒定律。 4 ）黑洞热力学：基于纠缠的思想，构建了平坦时空和黑洞时空上的量子标量场的热力学。由此构建的黑洞时空纠缠热力学与经典黑洞热力学具有相同的结构。