A Possible Origin of Dynamical Gauge Field

动态规范场的可能起源

基本信息

批准号：
06640398
负责人：
KIKKAWA Keiji
金额：
$ 1.22万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06640398/
关键词：
Berry phase effect Induced gauge symmetry Dynamical gauge field Holonomy field Miniature multi-universe Unification of space and matter 宇宙の分岐・融合 Kaluza-Klein機構 Kaluza-Klein-理論 Berry-位相機構ゲージ対称性の誘導ホロノミー場

项目摘要

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

（1）诱导的仪表理论在大多数试图统一粒子相互作用的理论中，我们的成就总结如下。通常，人们通常假设在极高的能量区域中假设高规格对称性，然后引入赞助对称性分解以获得标准理论。在这个项目中，我们发现了一种新机制，即使理论在高能区域具有低规格对称性，也能够在低能区域诱导一些较高的量规对称性。这是与空间和浆果相效应的kaluza-klein压实相关的，我们从重力的模型开始，u（1）-Gauge Field A_M（M = 0,1,2，...，...，5）与6维中的Fermion Field相互作用。如果假设该空间被压缩成4维的Minkowski空间时乘以G属的二维Riemann表面，那么普通的Kaluza-Klein理论告诉我们，一个U（1）u（1）-Gauge field a_m（m = 0,1，...预计田野将在4维空间中出现。我们已经证明，如果紧凑的光谱在拓扑上是非平地的，例如带有G> 0属的Riemann表面，那么整体场就会产生一组新的复合规轨道。诱导量规场的自由度来自义务，而固体是U（1） - 轨距领域紧凑的空间尺寸组件的复合场，该领域最初是在模型中准备的。这是一个普通的字符串模型，但我们假设连接的字符串代表一个1+1维宇宙。宇宙被其他宇宙分散在两个或多个宇宙中。我们已经确认，当宇宙巨大时，它非常稳定，尤其是在宇宙中心周围。这意味着微值的发射发生在其边缘。然而，在宇宙上，没有发现低能量物质领域。宇宙中的所有局部兴奋都是普朗克能量的顺序。在分析了该模型之后，我们发现我们的时空和物质场的自由度都处于相同的基础上，因此空间和物质能够在单个理论中统一。较少的