Analytic Continuation of Thermal $N$-Point Functions from Imaginary- to Real-Energies

We consider thermal $n$-point Green functions in the framework of quantum field theory at finite temperature. We show how analytic continuations from imaginary to real energies relate these functions originally defined in the imaginary-time formalism to retarded and advanced real-time ones. The described method is valid to all orders of perturbation theory. It has the further advantage that it is independent of approximations often applied in actual finite-order calculations.