权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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

4 维正则量子引力石中的可观测量结构和动力学

基本信息

批准号：
05640340
负责人：
KODAMA Hideo
金额：
$ 1.28万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

项目摘要

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.

在这项研究中，我们构建了完全约束系统的量子理论的新公式，以解决四维正则量子引力中时间变量和动力学处理的主要困难之一。在这个公式中，量子约束施加在一个无约束的状态空间上的相对振幅泛函上，这与传统的狄拉克方法不同，在狄拉克方法中，约束施加在状态向量本身上以拾取物理状态。这种修改使我们能够将时间变量纳入观测量，并将动态描述为无约束状态空间中因果子空间之间的映射。我们研究的一个重要成果是证明了这种形式主义中动力学的一致性。其主要思想是利用冯诺依曼代数的特殊子代数，由其中心分解得到的运动常数，拿起一个特殊的家庭的因果子空间称为IPAS。我们严格证明了，如果运动常数的von Neumann代数是I型的，则IPAS之间的动力学映射是共形的，这保证了一致性。此外，通过将这种形式主义应用于具有单一约束的系统（包括迷你超空间模型），我们已经证明它们的动力学具有与没有约束的普通量子力学系统相同的结构。