Pion propagation in real time field theory at finite temperature

We describe how the thermal counterpart of a vacuum two-point function may be obtained in the real time formalism in a simple way by using directly the 2×2 matrices that different elements acquire in this formalism. Using this procedure we calculate the analytic (single component) thermal amplitude for the pion pole term in the ensemble average of two axial-vector currents to two loops in chiral perturbation theory. The general expressions obtained for the effective mass and the decay constants of the pion are evaluated in the chiral and the non-relativistic limits. PACS 11.10.Wx; 12.38.Mh; 12.39.Fe