Formulation of Conservation Law of Energy for Electron Field in Tensor Formalism

In previous works, Dirac equation for half-spin particle has been written in tensor form, in the form of non-linear Maxwell's like equations through two isotropic complex vectors F=E+iH and F'=E'-iH'. The complex vectors F=E+iH and F'=E'-iH' satisfy non-linear condition F.F=0, equivalent to two conditions for real quantities E.E-H.H=0 and E.H=0, obtained by equating to zero separately real and imaginary parts of equality F.F=0. It has been proved, that the vectors E and H have the same properties as those of E, H, components of electromagnetic field.In this work, in order to understand these non-linear equations, we investigated the deducted from them law of conservation of energy for electron field