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

TL;DR

This paper investigates the fundamental properties of multi-particle Green and vertex functions in Keldysh formalism, emphasizing causality, thermal equilibrium conditions, and the consistency of approximation methods in nonequilibrium condensed matter physics.

Contribution

It provides a comprehensive derivation of real-time properties of multi-particle functions in Keldysh formalism, including their analytic and equilibrium characteristics.

Findings

Derived general properties of multi-particle Green and vertex functions.

Analyzed causality and Kubo-Martin-Schwinger conditions in Keldysh formalism.

Discussed how diagrammatic and renormalization group approximations respect these properties.

Abstract

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.