Properties of multi-particle Green's and vertex functions within Keldysh formalism

The increasing interest in nonequilibrium effects in condensed matter theory motivates the adaption of diverse equilibrium techniques to Keldysh formalism. For methods based on multi-particle Green's or vertex functions, this involves a detailed knowledge of the real-time properties of those functions. In this review, we derive general properties of fermionic and bosonic multi-particle Green's and vertex functions for a stationary state described within Keldysh formalism. Special emphasis is put on the analytic properties associated with causality and on a detailed discussion of the Kubo–Martin–Schwinger conditions which characterize thermal equilibrium. Finally we describe how diagrammatic approximations and approximations within the functional renormalization group approach respect these properties.