About Asymmetric, Symmetric and Antisymmetric Tensors of the Electromagnetic Field and Maxwell's Equations

The asymmetric and symmetric tensors can be associated with to the electromagnetic field (EMF) canonical antisymmetric tensor. From these tensors, in the form of their divergences, new EMF equations of follow. The introduction of field sources into Maxwell's equations is mathematically incorrect, since these equations are a four-dimensional divergence with respect to one of the indices of the four-dimensional rotor (antisymmetric tensor). The total divergence of the antisymmetric EMF tensor is equal to the sum of divergences for each of its indices. These divergences have different signs, and their sum is identically zero. Thus, EMF sources can only be attributed to the total divergence of asymmetric or symmetric EMF tensors, the full divergences of which can be non-zero. As a result, it can be argued that Maxwell's equations do not carry a real physical meaning and should be replaced by field equations that follow in the form of a four-dimensional divergence from the symmetric EMF tensor. Only these EMF equations can be attributed to the field sources. These equations represent a new complete system of EMF equations, replacing the system of Maxwell's equations. From the symmetric EMF tensor follows the dynamic Navier-Stokes equation for the vector potential showing the unity of the field and the continuum.