Relativistic Hydrodynamics Equivalent to the Dirac Equation

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In our previous articles the hydrodynamical structures of the wave equations in quantum mechanics or field theory have been investigated in detail for the cases of relativistic scalar equation1> (Klein-Gordon equation) on the one hand and of non-relativistic spinor equation2> on the other. As was remarked there2>, a similar method can be applied to the case of Dirac wave equation. For this purpose we must first consider the kinematical problem to find out the set of tensor quantities under suitable subsidiary conditions which represents the Dirac spinor 1/J in a physically meaningful way. As such quantities we first take up the 16 density functions,

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