  An analysis of the Wigner function for identical particles is presented. Four
situations have been considered. i) A scattering process between two
indistinguishable electrons described by a minimum uncertainty wave packets
showing the exchange and correlation hole in Wigner phase space. ii) An
equilibrium ensemble of N electrons in a one-dimensional box and in a
one-dimensional harmonic potential showing that the reduced single particle
Wigner function as a function of the energy defined in the Wigner phase-space
tends to a Fermi distribution. iii) The reduced one-particle transport-equation
for the Wigner function in the case of interacting electrons showing the need
for the two-particle reduced Wigner function within the BBGKY hierarchy scheme.
iv) The electron-phonon interaction in the two-particle case showing
co-participation of two electrons in the interaction with the phonon bath.
