or The ordinary Maxwell’s equation system, describing an electromagnetic field (in vacuum), generated by the current density of electrical charges j$_{e}$ , can be written as Since the result of action of operator ∂ 2 ∂x $^{i}$∂xk (symmetric with respect to indices i, k ) on antisymmetric tensor F ik A$_{e}$ (similar to any convolution of symmetric tensor with the antisym- metric one) identically equals zero, the continuity equation describing the charge conserva- tion law follows from (4b): In quantum field theory, equation (4b) is replaced, according to definition (1), by the following equation: In the equation (4a) instead of tensor F$_{A}$$_{e}$ pseudo-tensor dual to tensor F$_{A}$$_{e}$ , may be used, where e iklm is the absolutely antisymmetric, unit, four- dimensional pseudo-tensor of the fourth rank with weight W = +1, which components change their signs with permutation of any two indices and by definition (pseudo-tensor e$_{iklm}$ has weight W = − 1 and e 0123 = − 1). With x coordinate system replaced by ¯ x coordinate system (caused by changes in the basis of n -dimensional 4 F ik A$_{e}$ =    0 − E 1 e − E 2 e − E 3 e E 1 e 0 − H 3 e H 2 e E 2 e H 3 e 0 − H 1 e E 3 e − H 2 e H 1 e 0    F$_{A}$$_{e}$$_{ik}$ =    0 E 1 e E 2 e E 3 e − E 1 e 0 − H 3 e H 2 e − E 2 e H 3 e 0 − H 1 e − E 3 e − H 2 e H 1 e 0   $^{.}$ (3) ∂j i e ∂x i = 0 . (5) − ∂$_{k}$∂ $^{k}$Ai e + ∂$_{k}$∂ $^{i}$Ak e def = □ A i e + ∂$_{k}$∂ $^{i}$Ak e = − 4 π c j i $_{e}$. (6) F ⋆ ik A$_{e}$ def = 1 2! e $^{iklm}$F$_{A}$$_{e}$$_{lm}$ , (7) e 0123 def = + 1 , (8) ∂F ik A$_{e}$ ∂x$_{l}$ + ∂F kl A$_{e}$ ∂x$_{i}$ + ∂F li A$_{e}$ ∂x$_{k}$ = 0 , (4a) ∂F ik A$_{e}$ ∂x k = − 4 π c j i $_{e}$. (4b)