Manifestations of Bose and Fermi statistics on the quantum distribution function for systems of spin-0 and spin-½ particles

We consider the manifestations of Bose and Fermi statistics on the original quantum distribution function. Initially, we consider some general symmetry properties of the density matrix. Next, we convert these results into distribution-function language for the case of a system of spin-0 particles. Finally, we consider a system of spin-½ particles, for which we treat the combined effects of both spin and statistics.