A Possible Origin of Dynamical Gauge Field

我们的成就在这项赠款的支持下已被总结为后续。（1）诱导的高斯理论中大多数的理论是试图统一粒子的相互作用，一个通常的假设是在一个极高能量区域的高高斯对称性，然后提出一个自发的对称性突破以获得标准理论。在这个项目中，我们发现了一种新的机制，即使理论在高能量区域也有低增益对称性，而在低能量区域也有可能被诱导。这是在与空间和浆果相位效应的卡卢扎-克莱因兼容性的连接中，我们从重力和U （1）-盖格字段A_M， （M=0，1，2，...， 5）与6-尺寸内的一个fermion字段交互。如果一个假设使空间适应4维Minkowski空间时间为2维Riemann表面与G代，然后正常的Kaluza-Klein理论告诉我们一个U （1）-gauge字段A_M， （M=0，1，...， 3），两个Kaluzz ... More A-Klein U （1）--Gauge场来自测量张量，而4个标量场预计会出现在4个维度空间。我们有一个证明，如果一个紧凑的规格在拓扑上是非琐事的，就像一个带有G>0的Riemann表面一样，然后生成一套新的复合GaugeFields。受诱导的高斯场的自由程度来自于空心体，而空心体是U （1）的复合空间维度组件的复合场--高斯场最初是在模型中准备的。（2） A miniature model of multi universes to understand a possible theory of everything， we have studed a miniature model generating multi universes。这是一个普通的字符串模型，但我们认为字符串的连接部分代表一个1+1维度宇宙。宇宙，当被另一个宇宙分散时，分裂成两个或许多个宇宙。我们已经确认，当宇宙是巨大的，它是非常稳定的，特别是围绕着宇宙中心。这一启示是，微宇宙的使命在它的边缘出现;在宇宙中，无论如何，都发现了低能量物质场;宇宙中的所有地方兴奋都是普朗克能量的秩序。通过对这个模型的分析，我们发现了一个可能的因素，即我们的空间-时间和物质场的自由程度都是在同一个脚上，所以空间和物质都可以在一个单一的理论中统一。Less（低）

Our achievements under the support of this Grant are summarized as follows.(1) Induced gauge theoryIn most of theories which try to unify the particle interactions, one usually assumes a high gauge symmetries in an extremely high energy region, then one introduces a spontaneous symmetry breakdown to get the standard theory. In this project we found a new mechanism that even if a theory has a low gauge symmetry in high energy region, some higher gauge symmetry is able to be induced in low energy region. This is nicely realized in connection with the Kaluza-Klein compactification of the space and the Berry phase effect.We started off from a model of the gravity and U (1) -gauge field A_M, (M=0,1,2, ・・・, 5) interacting with a fermion field in 6-dimensions. If one assumes that the space is compactified into a 4-dimensional Minkowski space times a 2-dimensional Riemann surface with genus G,then ordinary Kaluza-Klein theory tells us that one U (1) -gauge field A_M, (M=0,1, ・・・, 3), two Kaluz … More a-Klein U (1) -gauge fields comming from the metric tensor, and 4 scalar fields are expected to come out in 4-dimensional space. We have demonstrated that if the compactified spece is topologically non-trivial such as the Riemann surface with genus G>0, then the holonomy fields generate a set of new composite gauge fields. The degrees of freedom of the induced gauge fields come from the holonomies, and the holonomies are composite fields of the compactified space dimensional components of the U (1) -gauge field which is originally prepared in the model.(2) A miniature model of multi universesTo understand a possible theory of everything, we have studied a miniature model generating multi universes. This is an ordinary string model, but we assume that a connected piece of string represents a 1+1 dimensional universe. The universe, when scattered by other universe, splits up into two or many universes. We have confirmed, when the universe is gigantic, it is quite stable especially around the center of the universe. This implies that the emission of micro-universes occurs at the edge of it. On the universe, however, no low energy matter fields are found. All the local excitation in the universe are of the order of the Planck energy. Having analyzed this model we have found a possibility that our space-time and the matter field degrees of freedom are all on a same footing, so that the space and the matter are able to be unified in a single theory. Less