  In recent work we developed a description of cosmic large scale structure
formation in terms of non-equilibrium ensembles of classical particles, with
time evolution obtained in the framework of a statistical field theory. In
these works, the initial Gaussian correlations between particles have so far
been treated perturbatively or restricted to pure momentum correlations. Here
we treat the correlations between all phase-space coordinates exactly by
adopting a diagrammatic language for the different forms of correlations,
directly inspired by the Mayer cluster expansion. We will demonstrate that
explicit expressions for phase-space density cumulants of arbitrary $n$-point
order, which fully capture the non-linear coupling of free streaming kinematics
due to initial correlations, can be obtained from a simple set of Feynman
rules. These cumulants will be the foundation for further investigations of
interacting perturbation theory.

Statistical Mechanics;Cosmology and Nongalactic Astrophysics