Kaluza-Klein和规范理论中的塞曼拓扑
On Zeeman Topology in Kaluza-Klein and Gauge Theories
摘要：
E. C.塞曼[1]批评了这样一个事实，即在所有的文章和书籍，直到那一刻（1967年）的拓扑工作与闵可夫斯基空间是欧几里德。他提出了一个新的拓扑，这是推广到更一般的时空格贝尔[2]。在时空的塞曼拓扑和格贝尔拓扑中，唯一连续曲线分别是由类时直线和测地线组成的曲线。在他的论文中，格贝尔提出了一种拓扑结构，其连续曲线是由带电粒子运动组成的曲线。在这里，我们通过应用卡鲁扎-克莱因理论的投影定理（Bleecker [3]第144页），以非常简单的方式得到了这种拓扑的推广，对任何规范场都有效。这种方法涉及塞曼拓扑和卡鲁扎-克莱因，因此规范理论，什么带来的见解和点的方向，一个完全的几何理论。
英文摘要：
E. C. Zeeman [1] has criticized the fact that in all articles and books until that moment (1967) the topology employed to work with the Minkowski space was the Euclidean one. He has proposed a new topology, which was generalized for more general space-times by Goebel [2]. In the Zeeman and Goebel topologies for the space-time, the unique continuous curves are polygonals composed by time-like straight lines and geodesics respectively. In his paper, Goebel proposes a topology for which the continuous curves are polygonals composed by motions of charged particles. Here we obtain in a very simple way a generalization of this topology, valid for any gauge fields, by employing the projection theorem of Kaluza-Klein theories (page 144 of Bleecker [3]). This approach relates Zeeman topologies and Kaluza-Klein, therefore Gauge Theories, what brings insights and points in the direction of a completely geometric theory.
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