The structure of the perturbation series of the spin-1 Bose gas at low temperatures
The properties of Green's functions and various correlation functions of density and spin operators are considered in a homogeneous spin-1 Bose gas in different phases. The dielectric formalism is worked out and the partial coincidence of the one-particle and collective spectra is pointed out below the temperature of Bose-Einstein condensation. As an application the formalism is used to give two approximations for the propagators and the correlation functions and the spectra of excitations including shifts and widths due to the thermal cloud.