亥姆霍兹定理与超光速信号
The Helmholtz Theorem and Superluminal Signals
摘要：
文献[1]指出，将矢量场分解为纵向（势）和横向（涡）分量的传统方法（亥姆霍兹定理）不适用于含时矢量场，特别是不适用于麦克斯韦方程组的延迟解。因此，根据[1]，[2]中基于亥姆霍兹定理得出的一些结论是错误的。本文证明了亥姆霍兹定理对任意矢量场都是成立的，无论是静态的还是含时的。因此，[1]中质疑的文献[2]的结论是正确的。Helmholtz定理在一般情况下的有效性是由于矢量场的上述分解不影响场的时间坐标，因而场的时间坐标在分解过程中起着被动的作用。对文[1]中的错误进行了分析。注意，对于点粒子，电场的纵向和横向分量，分别取，其特征在于无限大的传播速度。然而，总电场的表达式的超光速的贡献相互抵消。
英文摘要：
The conventional decomposition of a vector field into longitudinal (potential) and transverse (vortex) components (Helmholtz's theorem) is claimed in [1] to be inapplicable to the time-dependent vector fields and, in particular, to the retarded solutions of Maxwell's equations. Because of this, according to [1], a number of conclusions drawn in [2] on the basis of the Helmholtz theorem turns out to be erroneous. The Helmholtz theorem is proved in this letter to hold for arbitrary vector field, both static and time-dependent. Therefore, the conclusions of the paper [2] questioned in [1] are true. The validity of Helmholtz's theorem in the general case is due to the fact that the decomposition above of vector field does not influence the field time coordinate, which plays, thus, a passive role in the decomposition procedure. An analysis is given of the mistakes made in [1]. It is noted that for point particle the longitudinal and transverse components of electric field, taken separately, are characterized by the infinitely great velocity of propagation. However, superluminal contributions to the expression for the total electric field cancel each other.
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