Quantum Gravity by the Complex Canonical Theory and its Application to Cosmology
Project/Area Number  02640228 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
KODAMA Hideo College of Liberal Arts and Sciences Associated Professor, 教養部, 助教授 (40161947)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1991 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1990 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Quantum gravity / General relativity / Cosmology / Complex canonical theory / Ashtekar formalism / Bianchi models / 量子重力 / 一般相対論 / 宇宙論 / 複素正準理論 / アシュラカ形式 / ビアンキモデル / 一般相対性理論 / アシュテカ形式 / アシュチカ形式 
Research Abstract 
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 nonvanishing cosmological constant. This solution is the first exact solution that describes the quantum behavior of generic spacetimes. Though it corresponds to the HartleHawking'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. 以上の研究成果はPhysical Review D誌、第6回マルセルグロスマン国際会議、Reports in Astrophysics & Cosmology誌(出版予定)に発表された。

Report
(4results)
Research Output
(14results)