  We derive a non-perturbative, closed, analytic equation for the non-linear
power spectrum of cosmic density fluctuations. This result is based on our
kinetic field theory (KFT) of cosmic structure formation and on evaluating
particle interactions in the Born approximation. At redshift zero, relative
deviations between our analytic result and typical numerical results are ~ 15 %
on average up to wave numbers of k <= 10 h/Mpc. The theory underlying our
analytic equation is fully specified once the statistical properties of the
initial density and momentum fluctuations are set. It has no further adjustable
parameters. Apart from this equation, our main result is that the
characteristic non-linear deformations of the power spectrum at late cosmic
times are determined by the initial momentum correlations and a partial
compensation between diffusion damping and particle interactions.
