Pion field in nuclear matter near the critical point of the π-condensate instability

General expressions are obtained for the polarization operator PI and the pion Green function D with account for the ππ interaction in nuclear matter. Properties of PI near the critical point of the pionic condensation in the isotropical nuclear matter are investigated, for zero temperature, T=0, as well as T not equal to 0. It is shown that the operator PI calculated with account for the ππ interaction, has no singularities at T=0, due to fluctuations of the pion field. Meanwhile, at T not equal to 0 a rise of the thermal fluctuations near the critical point results in a divergence of PI. Conditions under which an account for the simplest graphs only is sufficient to calculate PI, are elucidated