Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken λϕ^4 theory, to the derivation of the threshold amplitude for the production of $n$ scalar particles by $n$ initial particles. The leading contributions to the tree amplitude, which become singular in the threshold limit, exhibit a factorial growth with n.

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