A. Yu. Ivanov, P. A. Andreev, L. S. Kuzmenkov
Based on the Darwin's Hamiltonian the many particle quantum hydrodynamics is considered. Force field appearing in the corresponding Euler equation is considered in details, contribution of different terms of the Darwin's Hamiltonian in the Euler equation is traced. For example, relativistic correction to particle kinetic energy leads to several terms in the Euler equation, these terms have different form, and one of them has form looking like a term appearing from the Darwin term. So, two different mechanisms give analogous contribution in wave dispersion, which differ by sign of terms. Microscopic analog of the Biot-Savart law, called current-current interaction, and describing interaction of moving charges via magnetic field, is also included in our description. The semi-relativistic generalization of the quantum Bohm potential is obtained. Contribution of relativistic effects in the spectrum of plasma collective excitations is considered.
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http://arxiv.org/abs/1209.6124
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