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

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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 or vertex functions this involves a detailed knowledge of the real-time properties of those functions. In this paper, we derive general properties of fermionic and bosonic multi-particle Green 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 characterise thermal equilibrium. Finally we describe how diagrammatic approximations and approximations within the functional renormalisation group approach respect these properties.