Field Theory and Gravity-foundation and applications

阐明了场论和引力的各种性质。标量场论中可能同时存在真真空和假真空。在一系列论文中表明，如果块内有费米子耦合到标量场，块内和块外分别是伪真空和真真空的块解就会变得稳定。汤川遥菜的互动起着重要作用。这些团块可能是在早期宇宙中产生的，也可能是现在观测到的暗物质的很好候选者。发现在温伯格-萨拉姆-爱因斯坦理论中，如果宇宙的空间拓扑是封闭的，那么自然会出现杨-米尔斯场和希格斯场相互缠绕的位形。随着宇宙的膨胀，这种结构变得不稳定。在弛豫到更稳定组态的过程中，可以产生较大的磁场。在定义在轨道上的大统一理论中，规范对称性的动态重排是通过Hosotani机制发生的。边界条件形成等价类。在每个等价类中，由于量子效应，得到的物理结果是相同的，而不考虑所选择的边界条件。文中还提出了选择一类等价的边界条件，使其能量密度最低。然而，在最小模型中，标准模型的对称性是不被选择的。在弦理论中，时空维度是10维，但观测到的维度是4维。额外的六个维度必须保证弦理论中的Weyl不变性。证明了存在非平凡的六维曲线空间，其中B场不为零。

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.