Retarded Greens Functions and Forward Scattering Amplitudes in Thermal Field Theory

In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time formalism. Furthermore, we give a simple calculational method for evaluating the temperature dependent parts of the retarded vertex functions, to one loop, by identifying them with the forward scattering amplitudes of on-shell thermal particles. As an application of the method, we calculate and show that the temperature dependent parts of all the retarded functions vanish at one loop order for 1+1 dimensional massless QED. We further point out that, in this model, in fact, the temperature dependent parts of all the retarded vertex functions vanish to all orders in perturbation theory.