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.Comment: 34 pages, 17 figure
