Quantum gravity in 2+epsilon dimensions and renormalization group
Project/Area Number  06640380 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
素粒子・核・宇宙線

Research Institution  Tokyo Institute of Technology 
Principal Investigator 
KITAZAWA Yoshihisa Tokyo Institute of Technology, Faculty of Science, Assistant Professor, 理学部, 助教授 (10195258)

Project Period (FY) 
1994 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1996 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1995 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1994 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Quantum Gravity / 2+epsilon dimensional Expansion / Renormalizability / Scale Invariance / Scaling Exponent / 繰り込み能性 / くり込み可能性の証明 / 2ループレベルの量子補正 / 共変な計算方法 / 重力の量子化 / くりこみ群の紫外固定点 / オーダーパラメーター / 2+ε次元の量子重力 / くりこみ可能 / 量子重力の相転移 
Research Abstract 
The purpose of this research is to deepen our understanding of quantum gravity by the 2+epsilon demensional expansion method. The quantization of the gravitational interaction is the one of the principle problem in particle physics. The fundamental difficulty of this problem resides in the nonrenormalizability. We can avoid this problem by the 2+epsilon dimensional expansion method near two dimensions. The quantum gravity in 2+epsilon dimension is theoretically interesting due to this reason and may possess qualitatively similar feature with four dimensional qunatum gravity. I have constructed a proof of the renormalizabilty in a formalism which preserves the manifest volume preserving diffeomorphism with my collaborators. In this proof we have used the fact that the structure of the divergences which appear the the perturbative evaluation of the effective action is strongly constrained by the BRS invariance. The conformal invariance is broken by the quantum anomaly near two dimension. However its structure is well understood and the divergences have to be consistent with the anomaly. I have further performed an explicit calculation at the two loop level with my collaborator. We are able to calculate the scaling exponent of the gravitational coupling constant near the untraviolet fixed point of the space time which becomes the scale invariant. We have adopted a manifestly covariant calculation procedure and we are able to estimate a large quntum effect near such a fixed point. We are the first to derive the nontrivial scaling exponent at the fixed point in quantum gravity since thw two loop level calculation is necesarily for this purpose.

Report
(4results)
Research Output
(21results)