On a consistent macroscopic description for a spin quantum plasma with interparticle interactions

Quantum mechanical averaging of the particle concentration operator is an effective starting point for derivation of the many-particle quantum hydrodynamic equations. In many-particle quantum systems, we have to separate the ordered motion of the local center of mass (velocity field), the thermal, and the quantum motion. The quantum mechanical average process, invoked here, is completely determined, and is different from the usual averaging processes that introduces undefined probabilities for quantum states. It is shown that the Madelung decomposition for the $N$-particle spinor wave function allows the correct introduction of the velocity field, and gives explicit expressions for the quantum contributions to both the momentum, and the spin flux. The formalism also contains plasma effects produced by the Coulomb and spin-spin interparticle interactions. It is shown that both interactions appear in plasma dynamics as effective electric and magnetic fields. As result we find a fully coherent description for spin quantum plasma in the self-consistent field approximation for interparticle interactions. A simple consequence - the change brought about by interparticle correlations on the propagation of electrostatic waves in a spin quantum plasma - is discussed.