Kinetic Field Theory: Effects of momentum correlations on the cosmic
  density-fluctuation power spectrum
  In earlier work, we have developed a Kinetic Field Theory (KFT) for
cosmological structure formation and showed that the non-linear
density-fluctuation power spectrum known from numerical simulations can be
reproduced quite well even if particle interactions are taken into account to
first order only. Besides approximating gravitational interactions, we had to
truncate the initial correlation hierarchy of particle momenta at the second
order. Here, we substantially simplify KFT. We show that its central object,
the free generating functional, can be factorized, taking the full hierarchy of
momentum correlations into account. The factors appearing in the generating
functional, which we identify as non-linearly evolved density-fluctuation power
spectra, have a universal form and can thus be tabulated for fast access in
perturbation schemes.
  In this paper, we focus on a complete evaluation of the free generating
functional of KFT, not including particle interactions yet. This implies that
the non-linearly evolved power spectra contain a damping term which reflects
that structures are being wiped out at late times by free streaming. Once
particle interactions will be taken into account, they will compensate this
damping. If we suppress this damping in a way suggested by the
fluctuation-dissipation relations of KFT, our results show that the complete
hierarchy of initial momentum correlations is responsible for a large part of
the characteristic non-linear deformation and the mode transport in the
density-fluctuation power spectrum. Without any adjustable parameters, KFT
accurately reproduces the scale at which non-linear evolution sets in.
  Finally, we further develop perturbation theory based on the factorization of
the generating functional and propose a diagrammatic scheme for the
perturbation terms.
