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. 
F. T. Brandt, Ashok Das, J. Frenkel and A. J. da Silva