Spin rotational invariance and the thermal excitation of magnons at low temperatures

A low-temperature expansion for real-time thermal Green's functions for a system of spontaneously polarized spin-$\frac{1}{2}$ fermions is constructed using the formalism of thermo-field dynamics. The method is applied to consider the low-temperature corrections to various physical quantities arising from the thermal excitation of the magnons. In particular the way in which the leading corrections from such excitations may be obtained is demonstrated in an exact way from simple symmetry considerations independent of the particular model under consideration. The results obtained are compared with various approximate calculations.