在爱因斯坦的狭义相对论框架中用与运动质点轨迹相对应的基本场表示与运动质点相关联的场
Representation of fields associated with any moving point mass by means of fundamental fields corresponding to its trajectory in the frame of Einstein's special theory of relativity
摘要：
假设在洛伦兹坐标系中给定一个质点的相对论容许轨道。在这样一个框架中的一个事件可以用四个坐标来描述，前三个坐标代表事件的位置，最后一个坐标代表事件的时间。设G表示所有不在轨迹上的事件的集合。轨迹唯一地决定了集合G上的一个场系统，作者称之为基本场。最重要的是以下三个：（1）延迟时间场，表示波应该从轨迹发射到事件集合G的某个点的时间;（2）延迟时间场，表示事件的实际时间和延迟时间之间的差;（3）单位向量场，表示波应该发射的方向。在arXiv：0909.5240论文中，作者用基本场证明了修正后的费曼定律的场满足齐次麦克斯韦方程组，并得到了费曼场根据基本场的显式公式。本文证明了事件集G上的任何域都可以表示为上述三个域的函数。这三个域的联合值域表示与事件集G同构的可微流形M。流形由实数空间R、正实数空间和三维欧几里得空间中的单位球面的笛卡尔乘积组成。
英文摘要：
Assume that in a Lorentzian frame is given a relativistically admissible trajectory of a point mass. An event in such a frame can be described by four coordinates, first three representing the position and the last one the time of the event. Let G denote the set of all events that do not lie on the trajectory. The trajectory uniquely determines on the set G a system of fields called by the author the fundamental fields. The most important are the following three: (1) The retarded time field, representing the time a wave should be emitted from the trajectory to arrive at some point of the set of events G; (2) The delayed time field, representing the difference between the actual time of the event and the retarded time; (3) The unit vector field representing the direction in which the wave should be emitted. In the paper arXiv:0909.5240 the author used the fundamental fields to prove, that the fields of the amended Feynman's Law satisfy the homogeneous system of Maxwell equations, and to obtain explicit formulas for Feynman fields in terms of the fundamental fields. In this note the author proves that any field on the set G of events can be represented as a function of the three fields mentioned above. The joint range of these three fields represents a differentiable manifold M diffeomorphic with the set G of the events. The manifold consists of the Cartesian product of the space R of reals, the space of positive real numbers, and the unit sphere in 3 dimensional Euclidean space.
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