Structure of observables and dynamics in 4dimonsional canonical quantum grarit
Project/Area Number  05640340 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
素粒子・核・宇宙線

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
KODAMA Hideo Kyoto University, Yukawa Institute for Theoretical Physics, Professor, 基礎物理学研究所, 教授 (40161947)

Project Fiscal Year 
1993 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1995 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1994 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  general relativity / quantum gravity / canonical quantization / constrained system / von Neumann algebra / 一般相対論 / 量子重力理論 / 正準量子化 / 拘束系 / フォンノイマン代数 / 相対性理論 / 正準理論 / 量子重力 / 完全拘束系 / モジュライ空間 / 微分幾何学 
Research Abstract 
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 4dimensional 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.

Report
(5results)
Research Output
(23results)