A slightly relativistic fermion gas is described by the dynamical theory obtained from the Wigner distribution function. The problem is approached in a self-consistent manner including the two-body Darwin Hamiltonian. The goal is to find the departures from equilibrium and dispersion relations for wave propagation in the gas.

In this thesis a kinetic theory for spin-1/2 particles is given a brief overview, focusing on the derivation of an evolution equation for the quasiprobability distribution function used in the theory to describe certain types of quantum plasma. The current theory is expanded upon by exploring conservation laws. A local conservation law for momentum is derived using two different expressions for electromagnetic momentum, given by Abraham and Minkowski respectively. There has been some controversy over which of these expressions should be used; in the case considered here the expression given by Minkowski seems to be more suitable. Based on the conservation law for momentum, a conservation law for angular momentum is also derived.