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

## TL;DR

This paper introduces a diagrammatic method for ensuring positive spectral functions in many-body systems, extending previous equilibrium approaches to steady-state non-equilibrium conditions using retarded diagram products.

## Contribution

The authors develop an alternative half-diagram representation based on retarded diagrams, enabling the construction of positive spectral functions out of equilibrium.

## Key findings

- Ensures positive spectral functions in steady-state non-equilibrium systems.
- Extends equilibrium diagrammatic methods to non-equilibrium steady states.
- Provides a practical framework for spectral function analysis in complex systems.

## Abstract

Recently, a method was presented for constructing self-energies within many-body perturbation theory that are 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. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.