Аксиоматическое построение системы уравнений классической электродинамики

The classical electrodynamics equations for a stationary isotropic medium without polarization and magnetization effects with regard to possibility of collective motion for electric charges (vacuum), in contrast to traditional using the least action principle of classical theory of gage fields, are obtained from the postulate that alternating electromagnetic field can be described by a special relativity theory with two vector fields in Minkowski space (4-potential and 4-current). The condition of gage invariance for “power” vector fields in the classical electrodynamics defines antisymmetry of the 4-tensor electromagnetic field. The existence of two specific mathematical structures (pseudoand true vector in the three-dimensional space), whose components are the ones of the 4-tensor electromagnetic field, is determined. The postulate about two different “power” vector fields of the classical electrodynamics is a natural consequence of two different mathematical structures in the electromagnetic field tensor. The first pair of Maxwell equations (homogeneous equations) is obtained as a consequence of formal definition of corresponding vector fields. The second pair of Maxwell equations (inhomogeneous equations) is obtained as a consequence of the postulate that 4-current vector field is the vector “source” of the 4-tensor electromagnetic field. Vanishing of 4-divergence 4-current is shown to be the necessary condition of the theory concerned. The physical meaning of formally introduced “power” vector fields is determined. The fundamental equations of classical electrodynamics (Ampere’s circuital law and electromagnetic induction law) in the proposed approach are the consequence of the above-mentioned postulates