Study for Construction of Quantum Theory of Gravity

量子引力论的构建研究

• 批准号: 06640393
• 负责人: NINOMIYA Masao
• 金额: $ 1.34万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06640393/
• 关键词: Quantum Gravity; 2d Quantum Gravity; Renormalization Group; String Theory; String Field Theory; Conformal Field Theory; Random Surface; Quantum Black Hole; 一般相対性理論; 統一理論; ブラックホール

It is one of the main subjects in Modern Theoretical Physics to construct "Quantum Theory of Gravity" or "Quantum Gravity" from Gravitational Theory in General Theory of Relativity.M.Ninomiya studied in the past few years, in collaboration with Prof.H.Kawai (KEK) and Prof. Y.Kitazawa (Tokyo Inst.Technology), the theory as to how to construct Quantum Theory of Gravity by using the method of statistical field theory based on the renormalization group and epsilon expansion. We obtained several results which attracted attention not only in Japan but also overseas. Our method is unique in the sense that we begin to study the Einstein gravity in 2+epsilon dimensions near 2 dimensional space time where it becomes remormalizable, and then extend the resultant theory into realistic 4 dimensional space time through renormalization group.In 1996 we put forward our study in two directions. One of them is that we could prove renormalizability of our quantum gravity theory which was obtained in the past years. In this way our quantum gravity theory enables us to study the short distance behavior or high energy behavior of the space time structure. 2nd development in our study is that together with Y.Kitazawa we could perform the detail investigation of property of the space time near Big Bang singularity, which indicates birth of Universe. It is found that the space time has scaling property so that self-similarity holds. We plan to go to the study as to how to construct 4 dimensional Quantum Gravity.M.Fukuma showed that nonperturbative dynamical variables in matrix model (lattice gravity) is fermionic variable and it really represents solitonic object. He also obtained some interesting nonperturbative results.

从广义相对论中的引力理论构建“量子引力论”或“量子引力”是现代理论物理学的主要课题之一。 Kawai (KEK)和Y.Kitazawa教授(Tokyo Inst.Technology)关于如何利用统计场的方法构建量子引力论的理论基于重正化群和 epsilon 展开的理论。我们取得了不仅在日本而且在海外也引起关注的多项成果。我们的方法是独特的，因为我们开始研究二维时空附近的 2+epsilon 维度中的爱因斯坦引力，在那里它变得可重整化，然后通过重整化群将所得理论扩展到现实的 4 维时空。1996 年，我们将将我们的研究向两个方向推进。其中之一是我们可以证明过去几年获得的量子引力理论的可重整性。通过这种方式，我们的量子引力理论使我们能够研究时空结构的短距离行为或高能行为。我们研究的第二个进展是，与 Y.Kitazawa 一起，我们可以对大爆炸奇点附近的时空特性进行详细研究，这表明宇宙的诞生。发现时空具有标度性质，从而自相似性成立。我们计划去研究如何构造4维量子引力。M.Fukuma证明矩阵模型（晶格引力）中的非微扰动力学变量是费米子变量，它真正代表孤子物体。他还获得了一些有趣的非微扰结果。

项目成果

M.Fukuma: "Combinatorics of solitons in noncritical string theory" Physics Letters. B393. 316-320 (1997)

M.Fukuma：“非临界弦理论中的孤子组合”《物理快报》。

梅田敏明: "Conformal invarance and recormalization group in quantum gravity near two dimensions" Nuclear Physics. B427. 158-180 (1994)

Toshiaki Umeda：“二维附近量子引力中的共形不变性和重组群”核物理 158-180 (1994)。

福間將文: "Two dimensional quantum gravity in temporal gauge" Nuclear Physics. D427. 139-157 (1994)

Masafumi Fukuma：“时间规范中的二维量子引力”核物理 D427。

Y.Kitazawa: "Scaling behavior of Ricci curvature at short distance near two dimensions" Physical Review. D55. 2076-2081 (1997)

Y.Kitazawa：“二维附近短距离的里奇曲率的缩放行为”物理评论。

H.Awata: "Determinant formulae of quasi-finite representation of W_<1+*> algebra at lower levels" Physics Letters. B332. 336-344 (1994)

H.Awata：“低级 W_<1 *> 代数的准有限表示的行列式”《物理快报》。