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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

我们在这项资助下的成就总结如下：(1)诱导规范理论在大多数试图统一粒子相互作用的理论中，通常假设在极高的能量区域具有高规范对称性，然后引入自发对称破缺来得到标准理论。在这个项目中，我们发现了一个新的机制，即即使一个理论在高能区具有低规范对称，在低能区也能够诱导出一些更高规范对称。这在空间的Kaluza-Klein紧化和Berry相位效应中得到了很好的实现。我们从引力和U(1)规范场A_M，（M=0,1,2，·····，5）与6维费米子场相互作用的模型开始。如果假设空间被紧化成一个四维Minkowski空间乘以一个具有G格的二维Riemann曲面，那么普通的kaluja - klein理论告诉我们一个U(1) -规范场A_M，（M=0,1，····，3），两个Kaluz…更多来自度量张量的a- klein U(1) -规范场，以及4个标量场预计会出现在四维空间中。我们证明了如果紧化的类是拓扑非平凡的，如属G>0的Riemann曲面，那么完整场产生一组新的复合规范场。诱导规范场的自由度来源于完整集，完整集是模型中原制备的U(1) -规范场的紧化空间维度分量的复合场。为了理解一种可能的万有理论，我们研究了一个产生多宇宙的微型模型。这是一个普通的弦模型，但我们假设一段连接的弦代表一个1+1维的宇宙。当宇宙被其他宇宙分散时，就分裂成两个或多个宇宙。我们已经证实，当宇宙很大的时候，它是相当稳定的，尤其是在宇宙的中心附近。这意味着微宇宙的发射发生在它的边缘。然而，在宇宙中，没有发现低能物质场。宇宙中所有的局部激发都属于普朗克能量的量级。通过分析这个模型，我们发现了一种可能性，即我们的时空和物质场的自由度都在同一个基础上，这样空间和物质就可以统一在一个单一的理论中。少