The nonlinear field equation of the three-point correlation function of
  galaxies
  Based on the field theory of density fluctuation under Newtonian gravity, we
obtain analytically the nonlinear equation of 3-pt correlation function $\zeta$
of galaxies in a homogeneous, isotropic, static universe. The density
fluctuations have been kept up to second order. By the Fry-Peebles ansatz and
the Groth-Peebles ansatz, the equation of $\zeta$ becomes closed and differs
from the Gaussian approximate equation. Using the boundary condition inferred
from the data of SDSS, we obtain the solution $\zeta(r, u, \theta)$ at fixed
$u=2$, which exhibits a shallow $U$-shape along the angle $\theta$ and,
nevertheless, decreases monotonously along the radial $r$. We show its
difference with the Gaussian solution. As a direct criterion of
non-Gaussianity, the reduced $Q(r, u, \theta)$ deviates from the Gaussianity
plane $Q=1$, exhibits a deeper $U$-shape along $\theta$ and varies weakly along
$r$, agreeing with the observed data.
