论文标题
Kaluza-Klein理论的动力学机制
Dynamical mechanisms for Kaluza-Klein theories
论文作者
论文摘要
我们介绍了仪表理论和爱因斯坦的各种表述 - Yang-Mills方程在Kaluza-Klein理论的精神上。对于仪表工作，仅假定拓扑振动。对于重力加上量规场，没有假设振动：在尺寸的“时空” $ y $上定义了$ 4 + r $，而没有任何结构，其中$ r $是结构组的维度。如果后者是紧凑的，并且简单地连接，则经典的解决方案允许构建尺寸4的歧管$ x $作为物理时空，以至于$ y $ y $ y $ y $ y $ y $ y y $ y $ y $ x $ a $ x $的结构并导致了爱因斯坦的解决方案 - 扬·米尔斯系统。还讨论了爱因斯坦 - 马克斯韦尔系统的特殊情况：这足以使至少一个光纤闭合一个圆圈，以推断五维时空具有AFIBER束结构。
We present variational formulations of gauge theories and Einstein--Yang-Mills equations in the spirit of Kaluza-Klein theories. For gaugetheories, only a topological fibration is assumed. For gravitation coupled with gauge fields, no fibration is assumed: Fields are defined on a 'space-time' $Y$ of dimension $4 + r$ without any structure a priori, where $r$ is the dimension of the structure group. If the latter is compact and simply connected, classical solutions allow to construct a manifold $X$ of dimension 4 to be the physical space-time, in such a way that $Y$ acquires the structure of a principal bundle over $X$ and leads to solutions of the Einstein--Yang-Mills systems. The special case of the Einstein-Maxwell system is also discussed: It suffices that at least one fiber closes in on a circle to deduce that the five-dimensional space-time has afiber bundle structure.
