  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.

High Energy Physics - Theory