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

Abstract

The propagator of a virtual $\varphi$-field with emission of $n$ on-mass-shell particles all being exactly at rest is calculated at the tree-level in $\lambda {\varphi }^4$ 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 $2\to n$ are exactly vanishing at threshold for $n>4$ is thus given in the more conventional Feynman diagram technique.

Comments: 7 pages, LaTeX, TPI-MINN-92/46-T