Quantum Gravity by the Complex Canonical Theory and its Application to Cosmology

复杂正则理论的量子引力及其在宇宙学中的应用

基本信息

批准号：
02640228
负责人：
KODAMA Hideo
金额：
$ 0.9万
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：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

项目摘要

The results of the research during the period of two years are summarized as follows.1) We can construct a consistent framework for canonical quantum theories of totally constrained systems including general relativity only in terms of quantum constraints by extending the conventional framework of quantum mechanics.2) The canonical equation of motion is in general inconsistent with the reality condition if one formally quantizes the complex canonical theory. In the approach explained in 1), however, it is possible to construct a consistent theory by regarding the complex canonical theory as a special representation of the real triad formalism.3) I found an exact solution to all the quantum constraint equations in the complex canonical theory for the case of pure gravity with non-vanishing cosmological constant. This solution is the first exact solution that describes the quantum behavior of generic spacetimes. Though it corresponds to the Hartle-Hawking's wavefunction in the spatially homogeneous sector, it has one important new feature that it extends to the classically forbidden region and falls off there.4) The DeSitter spacetime is the unique Lorentzian WKB orbit described by this solution. In the cosmological context this suggests a picture that the universe described by a Lorenzian metric is created from an ensemble of Eulidean spacetimes.

在两年期间的研究结果总结如下。1）我们可以为完全受约束的系统的规范量子理论构建一个一致的框架，包括一般相对论，通过扩展量子机制的传统框架来通过量子限制来构建常规的量子框架。2）典型的方程与运动的一般不一致的条件是正式的，即一种正式的条件将一个正式的条件量化，即一种正式的条件量化了一种综合的条件。然而，在1）中解释的方法中，可以通过将复杂的规范理论作为真实三合会形式主义的特殊表示来构建一致的理论。3）我找到了一个精确的解决方案，可以解决复杂的规范理论中所有量子约束方程的精确解决方案，以纯粹的重力案例，具有非变化的宇宙常数。该解决方案是描述通用空间量子行为的第一个精确解决方案。尽管它对应于空间均匀扇区中Hartle-Hawking的波函数，但它具有一个重要的新功能，它扩展到经典的禁区，并落在那里。4）Desitter Spacetime是该解决方案所描述的独特的Lorentzian WKB轨道。在宇宙学的背景下，这表明了一张图片，即洛伦兹指标描述的宇宙是由欧利德（Eulidean）空间合奏创建的。