  Quantum plasma physics is a rapidly evolving research field with a very
inter-disciplinary scope of potential applications, ranging from nano-scale
science in condensed matter to the vast scales of astrophysical objects. The
theoretical description of quantum plasmas relies on various approaches,
microscopic or macroscopic, some of which have obvious relation to classical
plasma models. The appropriate model should, in principle, incorporate the
quantum mechanical effects such as diffraction, spin statistics and
correlations, operative on the relevant scales. However, first-principle
approaches such as quantum Monte Carlo and density functional theory or
quantum-statistical methods such as quantum kinetic theory or non-equilibrium
Green's functions require substantial theoretical and computational efforts.
Therefore, for selected problems, alternative simpler methods have been put
forward. In particular, the collective behavior of many-body systems is usually
described within a self-consistent scheme of particles and fields on the
mean-field level. In classical plasmas, further simplifications are achieved by
a transition to hydrodynamic equations. % Similar fluid-type descriptions for
quantum plasmas have been proposed and widely used in the recent decade. This
chapter is devoted to an overview of the main concepts of quantum hydrodynamics
(QHD), thereby critically analyzing its validity range and its main
limitations. Furthermore, the results of the linearized QHD in unmagnetized and
magnetized plasmas and a few nonlinear solutions are examined with
illustrations. The basic concepts and formulation of particle-particle
interactions are also reviewed at the end, indicating their possible
consequences in quantum many-body problems.
