Fluctuations properties and collective modes of quantum plasmas in a magnetic field

A complete set of equilibrium fluctuation formulas for the charge density, the momentum density and the energy density of a magnetized one-component quantum plasma is presented. The derivation is based on the use of equations of motion for Fourier-transformed imaginary-time Green functions. The resulting formulas depend both on the strength and the orientation of the magnetic field. They are a basic ingredient for the derivation of the collective-mode spectrum in the long-wavelength limit. Projection-operator methods are used to establish explicit expressions for the mode frequencies of a magnetized quantum plasma up to second order in the wave number