On the probability current density for neutral particles with 1/2 spin

Some specific properties of using real wave functions to describe neutral particles within the quantum mechanics framework are described. In particular basing on the Majorana representation solutions of Dirac equation as plane waves and Dirac 4-vector probability current jsup(k) are considered. It is shown that in the case under discussion jsup(k) (for particles with m not equal to 0 mass) is ''light vector'' jsup(k)jsub(k)=0