  The effect of the contribution of the vertical part of the real time path is
studied completely in the case of two points functions. Indeed, this vertical
part generally contributes in the calculation of a given graph. Moreover, this
contribution is essential in order to have a consistent equilibrium theory:
thanks to this contribution, the Green function are effectively invariant by
time translation, as they should be. As a by product, it is shown that the
perturbative calculations give a result which does not depend on the initial
time $t_I$ and final time $t_F$ of the path. The property of independence with
respect to $t_I$ is closely related to the KMS conditions, i.e. to the fact the
system is in thermal equilibrium. In the case of two point functions, the
contribution of the vertical part can be taken into account by the $n(|k_0|)$
prescription in the usual RTF Feynman rules.
