Formulation of Conservation Laws of Current and Energy for Neutrino Field in Tensor Formalism

In previous works, using Cartan map, Weyl's equation for neutrino has been written in vector form, in the form of non-linear Maxwell's like equations, through isotropic complex vector F=E+iH. The vector F=E+iH satisfies non-linear condition F.F=0, equivalent to two conditions for real quantities E.E-H.H=0 and E.H=0, obtained by separating real and imaginary parts in the equality F.F=0. It has been proved, that the vectors E and H have the same properties as the vectors E and H, components of electromagnetic field. In particular, the solution of these non-linear equations for free particle as well fulfils Maxwell's equations for vacuum (with zero at the right side). This allows us to interpret neutrino field as a new form of electromagnetic field. In this work, in studying the properties of this new electromagnetic field, we derived its laws of conservation of current and energy