Calculation of processes involving many particles at the kinematical threshold

A diagrammatic technique is derived for calculating processes involving the production of large numbers of particles. As an example, the amplitude of three particles scattering into $n$ particles at the kinematical threshold in $\lambda\phi^4$ theory is calculated. From the $3 \to n$ amplitude, it is seen that the one-loop amplitude for $2 \to n$ processes is suppressed by a factor of $1/n$.