Equation of motion for nonequilibrium Green functions

The equation of motion for nonequilibrium Green functions is derived within the framework of the Schwinger and Keldysh formalism of perturbation expan sion. For nonequilibrium distribution Green functions, the equation of moti on derived from quantum mechanics contains undefined singularities, whose e xplicit form depends on the specific initial or boundary condition. In the present work, the exact expression of singular terms is found in the equati on of motion from the time-looped perturbation theory in which the adiabati c initial condition is implied. Unlike the usual Dyson perturbation formali sm or the well known Kadanoff-Baym equation of motion, our resulting equati on can be adopted directly for calculations without the graphical analysis, which depends on the specific form of the Hamiltonian. On the basis of thi s equation of motion, the procedure of a nonperturbative solution is outlin ed and potential applications are briefly discussed.