Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit

Recently, a method was presented for constructing self-energies within many-body perturbation theory that is guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour [Phys. Rev. B 2014, 90, 115134]. An alternative half-diagram representation that is based on products of retarded diagrams is derived here. This approach extends the method to systems out of equilibrium. When a steady-state limit exists, it is shown that our approach yields a positive definite spectral function in the frequency domain.