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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.

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