Tensor Formulation of Dirac Equation through Divisors

Abstract

In previous works, spinor Dirac equation for half-spin particle has been written in tensor form, in the form of non-linear Maxwell's like equations through two complex isotropic vectors F=E+iH and F'=E'+iH'. It has been proved, that the fields E and H have the same properties as those of the electric and magnetic fields, which are components of a single 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 gives us the right to interpret electron field as a system of two electromagnetic fields (E,H) and (E',H'),  propagating with the phase velocity equal to the velocity of light and the velocity of the particle is the group velocity. In the present work, we shall write these non-linear Maxwell's like equations, representing Dirac equation in covariant form through divisors. This form directly reveals their relativistic invariance and open the possibilities to future generalizations.