Calculation of processes involving many particles at the kinematical threshold

Abstract

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 $\lambda {\varphi }^4$ 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 $1/n$.

Comments: 9 pages + 2 figures, TPI-MINN-93/01-T