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

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640228/
• 关键词: Quantum gravity; General relativity; Cosmology; Complex canonical theory; Ashtekar formalism; Bianchi models; 一般相対性理論; アシュテカ形式; アシュチカ-形式

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.

通过对传统量子力学框架的扩展，我们可以为包括广义相对论在内的完全约束系统的正则量子理论建立一个仅在量子约束下的相容框架; 2）如果对复正则理论进行形式量子化，正则运动方程一般与实际条件不一致.然而，在1）中所解释的方法中，通过把复正则理论看作是真实的三元组形式主义的一种特殊表示，可以构造一个相容的理论。3）对于宇宙学常数不为零的纯引力情形，我找到了复正则理论中所有量子约束方程的精确解。这个解是第一个描述一般时空量子行为的精确解。虽然它对应于Hartle-Hawking在空间均匀扇区中的波函数，但它有一个重要的新特征，即它延伸到经典禁戒区并在那里落下福尔斯。4）DeSitter时空是这个解描述的唯一Lorentzian WKB轨道。在宇宙学的背景下，这表明了一个图像，即由洛伦兹度规描述的宇宙是从欧几里得时空的系综中产生的。

项目成果

Hideo Kodama: "Holomorphic wave function of the Universe" Physical Review D. 42. 2548-2565 (1990)

Hideo Kodama：“宇宙的全纯波函数”物理评论 D. 42. 2548-2565 (1990)

Hideo Kodama: "Proceedings of the 6th MarcelーGrossmann Meetings,eds.H.Sato et al." World Scientific, 10 (1992)

Hideo Kodama：“第六届 Marcel-Grossmann 会议记录，H. Sato 等编辑，10 (1992)”

Hideo Kodama: "Quantum Gravity by the Complex Canonical Formulation" Reports in Astrophysics & Cosmology. (1992)

儿玉秀夫：天体物理学中的“复杂规范公式的量子引力”报告