Binary Collision Expansion of the ClassicalN-Body Green's Function

The explicit time integrations in the formal binary collision expansion of the classical $N$-body Green's function are performed to obtain a product of binary collision operators which bears a strong resemblance to the Mayer product of $f_{\mathrm{ij}}\text{'}\mathrm{s}$. These integrations are exact for hard-sphere interactions and are expected to be a good approximation for finite but short-range pair interactions. The resulting expansion can be averaged over configuration space to obtain a transport equation for a dense gas in analogy with the cluster expansion of the classical partition function.