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Since the result of action of operator ∂ 2 ∂x$_{i}$∂x$_{k}$ (symmetric with respect to indexes i, k ) on antisymmetric tensor F ik A$_{e}$ (similar to any convolution of symmetric tensor with the antisym- metric one) identically equals 0, the continuity equation describing the charge conservation law follows from (4b): 

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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 

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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 indexes and 

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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 vector space), components of pseudo-tensor T of weight W , which is r -times contra-variant and s -times co-variant, are transformed according to the law (see, for example, [9]): 

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In contrast to the ordinary tensor’s component transformation, there is a factor in the form of Jacobian of coordinate transformation 

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of power W in equation (9). By virtue of such factor components of tensor F$_{A}$$_{e}$ and (dual to them) components of pseudo-tensor F ⋆ $_{A$_{e}$}$, dual to F$_{A}$$_{e}$ , are transformed in the same way 

