Exponentiation of Multiparticle Amplitudes in Scalar Theories

It is argued that the amplitudes of the production of n soft scalar particles by one or a few energetic ones in theories like λϕ 4 has the exponential form, A n ∝ √ n ! exp[ 1 λ F ( λn, ǫ )], in the regime λ → 0, λn = fixed, ǫ = fixed, where ǫ 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.