On transport theory of Bose systems. I

The concept of thermodynamical correlation functions for non-equilibrium states used by Kadanoff and Baym in transport theory is generalized by means of Bogoliubov's quasi-averages in order to describe transport phenomena in systems with Bose-Einstein condensation. The one-particle Green's function is decomposed in one part describing the condensed particles and a second one describing the elementary excitations. The coupled equations of motion for these functions are derived and some consequences for the case of slowly varying disturbances are discussed.