Numerical study of multiparticle production in $\lambda {\phi }^4$ theory

We study multiparticle production in the unbroken $(3+1)$-dimensional $\lambda {\phi }^4$ theory using the semiclassical method of singular solutions. We show that the probabilities of these processes are exponentially suppressed in terms of a small coupling constant $\lambda \ll 1$ if the multiplicity of the final state is large: $n\gg 1$. At $n\ll {\lambda }^{-1}$ the probabilities agree with well-known perturbative results. At $n\gg {\lambda }^{-1}$ they are dominated by loop effects and decrease exponentially with $n$, as we show for the first time.