Neo Formulation of Quantum Gravity and its Dynamical Aspects.
Project/Area Number  05640332 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
素粒子・核・宇宙線

Research Institution  HOKKAIDO UNIVERSITY 
Principal Investigator 
KAWAMOTO Noboru Hokkaido Univ., Graduate school of Sci., Pro., 大学院理学研究科, 教授 (50169778)

Project Fiscal Year 
1993 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1995 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1994 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Quantum Gravity / ChernSimons / Topological Field Theory / Topological Gravity / 量子重力 / ChernSimons作用 / トポロジカルな場の理論 / トポロジカル重力 / Chern Simons actions / フラクタル構造 / 重力 / ChernSimous / フラクタル / 2次元重力 / C=0模型 / ChornSimans Action / コンフォーマル重力 
Research Abstract 
Recently I have been working on two different kinds of subjects : (1)Various applications of generalized gauge theory, which was formulated from generalized ChernSimons theory. (2)Fractal structures of quantum gravity, numerical and analytical investigations. There are already several results in our investigations but they are not yet in the form of published papers. This is partly because of my moving time from Tokyo to Sapporo for last one or two ysars. (1)We have succeeded to generalize the standard ChernSimons action in arbitrary dimensions. In the generalized gauge thoery approach, we have investigated how the quantization of our generalized ChernSimons theory works. We have succeeded to quantize gl (1, R) generalized ChernSimons action in two dimensions. The model is simple but highly nontrivial for the quantization because of the reducibility of the model. The most recent result in this direction is the connection of the generalized ChernSomons gauge theory to noncommutati
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ve algebra formulation of YangMills action. We have shown that WeinbergSalam model can be formulated in the generalized version of of ourgauge thory and have a direct connection with noncommmutative algebra formulation of gauge thorey. The theory is formulated in particular only by formsincluding matter fields. (2)In our previous work we have shown numerically that the fractal sructure is the fundamental nature of quantum gravity for c=2 model in two dimensions. In the later analytic investigations we have scceeded to obtain transfer matrix of two dimensional quantum surface, which makes it possible to calculate the fractal dimension of twodemensional gravity for c=0 model.Recently we have started another type of munerical investigations on twodimensional quantum gravity surface. This is an investigation of studying fractal structure from finite size scaling points of view. その他に、4次元のEinstein重力が4次元のChernSimons作用を用いて定式化できることも示して有り、またトポロジカルなParticle Field Theoryと一般化されたChernSimonsの作用の同等性の一般論も展開して有ります。この部分もまだ論文の形になっていません。 Less

Report
(5results)
Research Output
(9results)