Two-body collisions and mean-field theory: The Brueckner-Boltzmann equation

Starting from the BBGKY hierarchy of density matrices, a quantum mechanical Boltzmann equation, including a mean field, is derived. Both the mean field, which is of the well-known Brueckner-Hartree-Fock form, as well as the collision term are expressed in terms of the self-consistent Brueckner G-matrix. The relation with the generalized Boltzmann equation of Kadanoff and Baym is discussed. It is shown that the usual quantum mechanical theories like TDHF and Uehling-Uhlenbeck appear as limiting cases. (orig.)