Exponentiation of Multiparticle Amplitudes in Scalar Theories

Abstract

It is argued that the amplitudes of the production of $n$ soft scalar particles by one or a few energetic ones in theories like $\lambda {\varphi }^4$ has the exponential form, $A_n\propto \sqrt{n!}\exp [\frac{1}{\lambda }F(\lambda n,ϵ)]$, in the regime $\lambda \to 0$, $\lambda n=fixed$, $ϵ=fixed$, where $ϵ$ is the typical kinetic energy of outgoing particles. Existing results support this conjecture. Several new analytical and numerical results in favor of the exponential behavior of multiparticle amplitudes are presented.

Comments: Revtex 3.0, 45 pages, 11 figures (some requires bezier.sty, two postscript figures appended after \end{document}), INR-866/94