Hydrodynamical description of the Dirac equation

Abstract

By suppressing ψ-spinor and γ-matrices completely, the Dirac field is shown to be equivalent with a non-linear vector field, which is fully interpreted as defining a new kind of relativistic hydrodynamics of a spinning fluid. In this hydrodynamics, there appears, besides spin, an additional internal degree of freedom θ, which specifies the disparatenesses between rest charge density and proper mass density and also between velocity and momentum. The theory is described for the case of Dirac field under the action of Maxwell field, manifesting also the gauge-independent feature of the formulation.