  Dyson equation for the real two-time commutator retarded one-magnon Green
function of the ferromagnetically polarized XX chain is suggested following the
Plakida-Tserkovnikov algorithm. Starting from this result a low-temperature
integral representation for the corresponding magnon self energy is obtained by
the truncated form factor expansion however without any resummations. Within
the suggested approach the low-temperature asymptotics of the transverse
dynamical structure factor may be readily studied. Some obtained line shapes
are presented.
