Initial-Value Problem for Inhomogeneous Condensate: Gaussian Approximation and Beyond

Using many-body theory we develop a set of formally exact kinetic equations for inhomogeneous condensate and one-body observables. The method is illutrated for phi^4 field theory in 1+1 dimensions. These equations, when computed with the help of time-dependent projection technique, lead to a systematic mean-field expansion. The lowest and the higher order terms correspond to, respectively, the gaussian approximation and the dynamical correlation effect.