Multiparticle tree amplitudes in scalar field theory
Fernando T Brandt, Josif Frenkel
Abstract
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 λϕ4 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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