Polarization pion operator at a finite temperature

On the base of a linear tau model the microscopical theory for the description of pion freedom degrees in a nuclear matter with a random isotopic composition at finite temperature T not equal to 0 is developed. The polarization pion operator with account of S and P wave πN interaction, N resonance and nucleon correlations is constructed. The conditions of emergence and existence of pion condensate at T not equal to 0 are investigated. The critical temperature Tsub(c) of pion condensation as a function of nuclear matter density has been found. In the framework of a classical approach it is shown that at T << msub(π)(pion mass) pion condensation arises through phase transition of the second kind to the state with weak pion field and at T > or approximately msub(π) preferential is the possibility of phase transition of the first kind to the state with maximum permissible π-condensate field. It is shown that in a neutron matter there exists temperature region in which temperature increase contributes to pion condensation. The role of pion field thermal fluctuations is investigated. In contrast to standard phase transitions in case of pion condensation with periodic in space condensate field thermal fluctuations of the pion field turn to be much stronger and determine temperature dependence of the polarization operator not only at T approximately Tsub(c) but also at T << Tsub(c)