New methods for analyzing quantum field theories

分析量子场论的新方法

• 批准号: 04640286
• 负责人: KAWAI Hikaru
• 金额: $ 1.09万
• 依托单位: National Institution for High Energy Physics(KEK) (1993)The University of Tokyo (1992)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04640286/
• 关键词: quantum gravity; string theory; epsilon - expansion; renormalization group; R^2 - gravity; transfer matrix; fractal; nonperturbative effect; ノンクリティカル・ストリング; ストリングの場; R^2ラグランジアン; 2+ε次元量子重力; 時空のフラクタル構造; トランスファーマトリックス; Eー展開; superstringの非摂動効果

We developed and applied several new methods for analyzing quantum field theories. In particular, we considered quantum gravity and string theories, and constructed useful nonperturbative frameworks for investigating those systems. First of all, we developed and epsilon - expansion scheme for 2+ epsilon dimensional quantum gravity. Using this scheme, we studied scaling properties of higher dimensional quantum gravity. We next considered R^2 Lagrangian can be solved exactly both in the infrared and ultraviolet limits. Furtheremore, we invented a transfer metrix formalism that can be applied in the presence of quantum fluctuations of the space-time. Using this method, we exactly solved the problem of two-dimensional quantum gravity, and proved that the space-time has fractal structures. This method may be a powerful tool for analyzing nonperturbative effects of string theories. Some attempts in this direction are now in progress.

我们开发并应用了几种分析量子场理论的新方法。特别是，我们考虑了量子重力和弦理论，并构建了用于研究这些系统的有用的非扰动框架。首先，我们开发了2+ Epsilon尺寸量子重力的Epsilon-扩展方案。使用此方案，我们研究了更高维量子重力的缩放特性。接下来，我们认为可以在红外和紫外线限制中精确地解决r^2拉格朗日。逐渐摩托车，我们发明了一种传递的大都会形式主义，可以在时空的量子波动的存在下应用。使用这种方法，我们精确地解决了二维量子重力的问题，并证明了时空具有分形结构。该方法可能是用于分析字符串理论的非扰动效应的强大工具。现在正在进行一些方向的尝试。

项目成果

H.Kawai R.Nakayama: "Quantum R^2 Gravity in Two-dimensions" Phys.Lett.B306. B306. 224 (1993)

H.Kawai R.Nakayama：“二维量子 R^2 引力”Phys.Lett.B306。

M.Fukuma S.Hosono H.Kawai: "Lattice Topological Field Theovy in Two-Dimensions" Comm.in Math Physicsに掲載予定.

M.Fukuma S.Hosono H.Kawai：“二维格子拓扑场论” 计划在 Comm.in Math Chemistry 上发表。

N.Ishibashi, H.kawai: "String Field Theory of C(〕SY.ltoreq.〔)1 Noncritical Strings" Physic Letters B. 322. 67-78 (1994)

N.Ishibashi, H.kawai：“C(〕SY.ltoreq.〔)1 非临界弦的弦场论”《物理快报》B. 322. 67-78 (1994)

H.Kawai,Y.Kitazawa,M.Ninomiya,: "Scaling exponents in quantum grarity near two dimensions" Nuclear Physics B.

H.Kawai，Y.Kitazawa，M.Ninomiya，：“二维附近量子引力中的缩放指数”核物理 B.

H.Kawai Y.Kitazawa M.Ninomiya: "Scaling Exponents in Quantum Gravity Near Two-Dimensions" Nucl.Phys.B393. 280 (1993)

H.Kawai Y.Kitazawa M.Ninomiya：“二维附近量子引力的标度指数”Nucl.Phys.B393。