Remarks on "summing one-loop graphs at multiparticle threshold"

The propagator of a virtual φ field with the emission of n on-mass-shell particles all being exactly at rest is calculated at the tree level in λφ4 theory by directly solving recursion equations for the sum of Feynman graphs. It is shown that the generating function for these propagators is equivalent to a Fourier transform of the recently found Green's function within the background-field technique for summing graphs at threshold suggested by Brown. Also the derivation of the result that the tree-level on-mass-shell scattering amplitudes of the processes 2→n are exactly vanishing at threshold for n>4 is thus given in the more conventional Feynman-diagram technique.