Microscopic quantum dynamics approach to the dilute condensed Bose gas

We derive quantum evolution equations for the dynamics of dilute condensed Bose gases. The approach contains, at different orders of approximation, for cases close to equilibrium, the Gross-Pitaevskii equation and the first-order Hartree-Fock-Bogoliubov theory. The proposed approach is also suited for the description of the dynamics of condensed gases that are far away from equilibrium. As an example the scattering of two Bose condensates is discussed.