Dirac Theory in Hydrodynamic Form

We consider quantum mechanics written in hydrodynamic formulation for the case of relativistic spinor fields to study their velocity: within such a hydrodynamic formulation it is possible to see that the velocity as is usually defined can not actually represent the tangent vector to the trajectories of particles. We propose an alternative definition for this tangent vector and hence for the trajectories of particles, which we believe to be new and in fact the only one that is possible. Finally we discuss how these results are a necessary step to take in order to face further problems, like the definition of trajectories for the multi-particle systems.