Comment on “ Summing one - loop graphs at multi - particle threshold ”

The propagator of a virtual φ-field with emission of n on-mass-shell particles all being exactly at rest is calculated at the tree-level in λφ 4 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 Lowell 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.