  We develop the effective field theory of density fluctuations for a Newtonian
self-gravitating N-body system in quasi-equilibrium, apply it to a homogeneous
universe with small density fluctuations. Keeping the density fluctuation up to
the second order, we obtain the nonlinear field equation of the 2-pt
correlation \xi(r), which contains the 3-pt correlation and formal ultra-violet
divergences. By the Groth-Peebles hierarchical ansatz and the mass
renormalization, the equation becomes closed with two new terms beyond the
Gaussian approximation, and their coefficients are taken as parameters. The
analytic solution is obtained in terms of the hypergeometric functions, which
is checked numerically. With one single set of fixed two parameters, the
correlation $\xi(r)$ and the corresponding power spectrum P(k) match
simultaneously the results from all the major surveys, such as APM, SDSS,
2dfGRS, and REFLEX. The model gives a unifying understanding of several
seemingly unrelated features of large scale structure from a field-theoretical
perspective. The theory is worthy to be extended to study the evolution effects
in an expanding universe.
