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

Assume that in a Lorentzian frame is given a relativistically admissibletrajectory of a point mass. An event in such a frame can be described by fourcoordinates, first three representing the position and the last one the time ofthe event. Let G denote the set of all events that do not lie on thetrajectory. The trajectory uniquely determines on the set G a system of fields called bythe author the fundamental fields. The most important are the following three:(1) The retarded time field, representing the time a wave should be emittedfrom the trajectory to arrive at some point of the set of events G; (2) Thedelayed time field, representing the difference between the actual time of theevent and the retarded time; (3) The unit vector field representing thedirection 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 ofMaxwell equations, and to obtain explicit formulas for Feynman fields in termsof the fundamental fields. In this note the author proves that any field on the set G of events can berepresented as a function of the three fields mentioned above. The joint rangeof these three fields represents a differentiable manifold M diffeomorphic withthe set G of the events. The manifold consists of the Cartesian product of thespace R of reals, the space of positive real numbers, and the unit sphere in 3dimensional Euclidean space.