Superoperator Many-body Theory of Molecular Currents: Non-equilibrium   Green Functions in Real Time
  The electric conductance of a molecular junction is calculated by recasting the Keldysh formalism in Liouville space. Dyson equations for nonequilibrium many body Green's functions (NEGF) are derived directly in real (physical) time. The various NEGFs appear naturally in the theory as time ordered products of superoperators, while the Keldysh forward/backward time loop is avoided. 
U. Harbola and S. Mukamel