Binary collision expansion and partial green's functions of Kadanoff-Baym

A new formula for the binary collision expansion of the unitary operator U (t₂, t₁) is proposed. The formula is applied to the expansion of the partial Green's functions of Kadanoff-Baym in powers of the correct binary scattering amplitude. It is shown that certain linked diagrams of left-multidentate structure should be taken into account. The duration of the binary collision is seen to play an important role in the rigorous formulation. Upon neglecting this duration, a useful approximation is found for the analysis of correlations on a macroscopic time scale.