 It was further developed by later contributors such as O. V. Konstantinov and V. I. Perel.Extension to driven-dissipative open quantum systems is given in 

The Keldysh formalism provides a systematic way to study non-equilibrium systems, usually based on the two-point functions corresponding to excitations in the system.The main mathematical object in the Keldysh formalism is the non-equilibrium Green's function (NEGF), which is a two-point function of particle fields.