$S$-matrix representation of the finite temperature propagator in $\lambda\phi^4$-QFT

The two-point Green function of the massive scalar $(3+1)$-quantum field theory with $\lambda\phi^4$ interaction at finite temperature is evaluated up to the 2nd order of perturbation theory. The averaging on the vacuum fluctuations is separated from the averaging on the thermal fluctuations explicitly. As a result, the temperature dependent part of the propagator is expressed through the scattering amplitudes. The obtained expression is generalized for higher orders of perturbation theory.