Non-equilibrium statistical field theory for classical particles:
  Non-linear structure evolution with first-order interaction
  We calculate the power spectrum of density fluctuations in the statistical
non-equilibrium field theory for classical, microscopic degrees of freedom to
first order in the interaction potential. We specialise our result to cosmology
by choosing appropriate initial conditions and propagators and show that the
non-linear growth of the density power spectrum found in numerical simulations
of cosmic structure evolution is reproduced well to redshift zero and for
arbitrary wave numbers. The main difference of our approach to ordinary
cosmological perturbation theory is that we do not perturb a dynamical equation
for the density contrast. Rather, we transport the initial phase-space
distribution of a canonical particle ensemble forward in time and extract any
collective information from it at the time needed. Since even small
perturbations of particle trajectories can lead to large fluctuations in
density, our approach allows to reach high density contrast already at first
order in the perturbations of the particle trajectories. We argue why the
expected asymptotic behaviour of the non-linear power spectrum at large wave
numbers can be reproduced in our approach at any order of the perturbation
series.
