Dyson equations for green functions of electrons in open single-level quantum dot

The infinite system of differential equations for the nonequilibrium Green functions of electrons in a single-level quantum dot connected with two conducting leads is truncated by applying the mean-field approximation to the mean values of the products of four operators. As the result the system of Dyson equations for the two-point real-time nonequilibrium Green functions in the Keldysh formalism as well as that of the two-point imaginary-time Green functions are derived.