Abstract: In previous works, Weyl´s equation for neutrino has been written in tensor form, in the form of non-linear Maxwell´s like equations, through complex isotropic vector( F) ⃗=E ⃗+iH ⃗. It has been proved, that the complex vector F ⃗=E ⃗+iH ⃗ satisfies non-linear condition( F) ⃗^2=0, equivalent to two conditions for real quantities E ⃗^2-H ⃗^2=0 and( E) ⃗.H ⃗=0, obtained by separating real and imaginary parts in the equality( F) ⃗^2=0. Further, it has been proved, that Maxwell's equations can also be written through complex vector( F) ⃗=E ⃗+iH ⃗. However, in the general case, the solution of Maxwell's equations does not satisfy non-linear condition( F) ⃗^2=0. In this work, in the development of this new tensor formalism, we elaborated the Lagrange formalism for electromagnetic field in terms of complex isotropic vectors.
Keywords: Electromagnetic field, Lagrange formalism, complex isotropic vector.
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