Dielectric Tensor for a Quantum Plasma

The dispersive properties of a plasma in a uniform magnetic field are investigated using a quantum "distribution function" (Wigner function). The Wigner function is shown to satisfy the Boltzmann-Vlasov equation in the long-wavelength approximation. The dielectric tensor is evaluated at $T=0\mathrm{}°$K for waves propagating along and across the magnetic field. It is conjectured that a simple "quantized kinetic theory" is applicable in areas previously explored only by more sophisticated means.