Comment on "Summing One-Loop Graphs at Multi-Particle Threshold"

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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 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 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.