Relativistic Hydrodynamics of the Dirac Matter

Abstract

The hydrodynamical model of Dirac matter is formulated and clarified. The basic equations are cast in various forms. Some characteristic features of the hydrodynamics are the distinctions between proper mass density and rest particle density and also between particle momentum and velocity, primarily specified by the theta behaviors. The energy-momentum conservation law also manifests a new structure. This quantum effect is interpreted as mechanical stress and flow of heat taking place inside the fluid. The theory provides a new directly physical point of view concerning various transformation properties of the Dirac field. Furthermore it reveals a conspicious quasisymmetrical property of the Dirac field existing between velocity and spin. The theory is formulated for cases of Dirac matter under external electromagnetic field and also of interacting Dirac and electromagnetic fields. It is manifestly gage-independent in both cases. The theory is worked out only for the case of c-number Dirac field. The mathematical method is systematized to estublish how the Dirac field can be manipulated solely with the set of tensor quantities which are related to the Dirac spinor as its bilinear covariants. (N.W.R.)