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Field Theory and Gravity-foundation and applications

场论与重力——基础与应用

基本信息

批准号：
13640284
负责人：
HOSOTANI Yutaka
金额：
$ 2.11万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

Various properties in field theory and gravity were clarified.1. It is possible that there are both true vacuum and false vacuum in scalar field theory. It was shown in a series of papers that lump solutions, inside and outside of which are the false vacuum and the true vacuum, respectively, become stable provided there are fermions coupled to the scalar field inside the lumps. Yukawa interactions play an important role. These lumps can be produced in the early universe, or can be good candidates for dark matter observed now.2. It is found that in the Weinberg-Salam-Einstein theory there naturally arises a configuration in which Yang-Mills fields and Higgs fields intertwine each other, if the spatial topology of the universe is closed. As the universe expands, this configuration becomes unstable. In the course of the relaxation to more stable configurations large magnetic fields can be produced.3. In grand unified theory defined on orbifolds, dynamical rearrangement of gauge symmetry takes place through the Hosotani mechanism. Boundary conditions form equivalence classes. In each equivalence class the resultant physics is the same, irrespective of boundary conditons chosen, due to quantum effects. It is also proposed to select an equivalence class of boundary conditions which leads to the lowest energy density. In theminimal model, however, the symmetry of the standard model is not chosen.4. In string theory the spacetime dimensions are ten, but the observed dimensions are four. The six extra dimensions must guarantee the Weyl invariance in string theory. It is shown that there are nontrivial six-dimensional curved space in which the B field is nonvanishing.

阐明了场论和引力中的各种性质.在标量场理论中，真真空和假真空都是可能存在的。一系列的论文表明，在块的内部和外部分别是假真空和真真空的块解，只要有费米子耦合到块内部的标量场，就会变得稳定。汤川相互作用起着重要的作用。这些团块可能在早期宇宙中产生，也可能是现在观测到的暗物质的良好候选者。本文发现，如果宇宙的空间拓扑是封闭的，那么在Weinberg-Salam-Einstein理论中自然会出现杨-米尔斯场和希格斯场相互交错的组态。随着宇宙的膨胀，这种结构变得不稳定。在弛豫到更稳定的组态的过程中，可以产生大的磁场.在定义在轨道上的大统一理论中，规范对称性的动力学重排通过细谷机制发生。边界条件形成等价类。由于量子效应，在每个等价类中，无论选择什么边界条件，所得的物理学都是相同的。它还建议选择一个等价类的边界条件，导致最低的能量密度。然而，在简化模型中，没有选择标准模型的对称性.在弦理论中，时空的维度是10，但观测到的维度是4。六个额外的维度必须保证弦论中的外尔不变性。证明了存在非平凡的六维曲空间，其中B场是非零的。