Unified Theories of Space and Matter

空间与物质的统一理论

• 批准号: 04302015
• 负责人: KIKKAWA Keiji
• 金额: $ 7.04万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-04302015/
• 关键词: Quantum Gravity; Universal String Theory; Induction of Gauge Theory; Conformal Field Theory; XXZ-Spin Chain; Motion of Micro-Organism; Loop Correlation Function; Hawking's No Boundary Condition; 弦(紐)理論; 行列理論; ブラックホール; 2次元量子重力; 3次元量子宇宙; プランク質量

Our achievements under the support of this Grant are summarized into following three categories.(1)Quantum Gravity and StringsSince the theory of quantum gravity is unrenormalizable the perturbational approach is not permitted. To understand the dynamics of gravity, therefore, one frequently studies various model theories that reflect some aspects of the problem. The two dimensional conformal model and the matrix model are most popular approaches. In the latter one can sum up over all topologies of two dimensional manifolds and find non-perturbative solutions for correlation functions. Many of studies were made along this line under our project, among which here we quote the study of loop correlation amplitudes in a two dimensional universe. The one-loop correlation amplitude is nothing but the two-dimensional version of Hawking's no boundary universe amplitude.Some people studied the topological conformal field and gave a new geometrical interpretation to the topology sum over manifol … More ds. In the string theory existence of "the universal string theory" was studied. All the superstrings and the bosonic strings are able to be deduced as a result of successive spontaneous symmetry breakdown of the universal string theory.(2)Origin of Gauge SymmetryIn most of cases one assume a high gauge symmetry in an extremely high energy region, then introduces a spontaneous symmetry breakdown to get the standard or GUT theory. In this project we found a new mechanism that even if a theory had a low gauge symmetry in high energy, some higher gauge symmetry is generated in the low energy region. This happens when the Kaluza-Klein compactification of space is taken place. The basic mechanism working there is shown to be the Berry phase effect.(3)Applications of Mathematical Techniques developed in String Theory Conformal field theory, w-algebra and Bethe anzatz method were applied to various mathematical problems. One of them is the thorough study of the XXZ-Spin Chain Model. The model had been studied in case of attractive force, now the repulsive spin-chain was analyzed in detail. Another interesting example is an application of w-algebra to the study of the motion of micro-organisms. Less

我们在此资助下取得的成就可归纳为以下三个方面。（1）量子引力与弦由于量子引力理论是不可重整化的，因此不允许用微扰方法。因此，为了理解引力的动力学，人们经常要研究反映这个问题某些方面的各种模型理论。二维共形模型和矩阵模型是最常用的方法。在后者中，人们可以总结所有的拓扑结构的二维流形，并找到非微扰解决方案的相关函数。在我们的项目中，沿着这条路线进行了沿着许多研究，其中我们引用了二维宇宙中圈关联振幅的研究。单圈关联振幅只是Hawking无边界宇宙振幅的二维版本，有人研究拓扑共形场，对流形上的拓扑和给出了新的几何解释 ...更多信息 DS.在弦理论中，研究了“万有弦理论”的存在性。所有的超弦和玻色弦都可以作为普适弦理论的连续自发对称破缺的结果导出。（2）规范对称性的起源在大多数情况下，人们假定在极高能区存在高规范对称性，然后引入自发对称性破缺，从而得到标准或大统一理论。在这个项目中，我们发现了一个新的机制，即使一个理论在高能区具有低规范对称性，在低能区也会产生一些更高的规范对称性。这发生在空间的卡鲁扎-克莱因紧化发生时。在那里工作的基本机制被证明是Berry相位效应。（3）弦理论中发展的数学技术的应用共形场论、W-代数和Bethe anzatz方法被应用于各种数学问题。其中之一是对XXZ-自旋链模型的深入研究。该模型已经在吸引力的情况下进行了研究，现在详细分析了排斥自旋链。另一个有趣的例子是w-代数在研究微生物运动中的应用。少

项目成果

T.Eguchi: "“Two-dimensional Black Hole and c=1 Liouville theory"" Proceeding of Como Conference. (1993)

T.Eguchi：“二维黑洞和 c=1 刘维尔理论”，科莫会议记录（1993）。

K.Iida,H.Minakata,O.Yasuda: "“A Test of the Equivalence Principle by Long-Baseline Neutrino-Oscillation Experiments"" Mode.Phys.Lett.A8. 1037-1046 (1993)

K.Iida、H.Minakata、O.Yasuda：“通过长基线中微子振荡实验检验等效原理”Mode.Phys.Lett.A8 (1993)。

K.Kikkawa and H.Tamura: "“Dynamical Gauge Field induced by the Berry Phase Mechanism"" J.Modern Phys.A10. No.5 (1995)

K.Kikkawa 和 H.Tamura：“贝里相机制引起的动态规范场”J.Modern Phys.A10 (1995)。

H.Kunitomo: "“A Hierarchy of Super w Strings"" Prog.Theor.Phys.92(1994). 1019-1031 (1994)

H.Kunitomo：““超级 w 弦的层次结构””Prog.Theor.Phys.92(1994) 1019-1031 (1994)。

T.Kashiwa :""Berry's phase and Enclidean Path Integral"" Ann.of Phys.220. 248-273 (1992)

T.Kashiwa：““贝里相位和英克里得路径积分””Ann.of Phys.220。