Numerical study of multiparticle production in $\phi^4$ theory: comparison with analytic results

TL;DR

This paper introduces a numerical approach based on semiclassical methods to compute multiparticle production probabilities in scalar field theories, successfully reproducing known results in a specific regime.

Contribution

It develops a numerical method using semiclassical singular solutions to analyze multiparticle production in $\,\lambda\phi^4$ theory, extending previous analytic results.

Findings

Successfully reproduces known multiparticle production probabilities in the specified regime.

Validates the numerical method against existing analytical results.

Provides a new computational tool for studying multiparticle processes in quantum field theories.

Abstract

We develop a numerical method to compute the probabilities of multiparticle production in weakly coupled scalar theories. Our technique is based on D.T. Son's semiclassical method of singular solutions. Applying it to the process $1 \to n$ in the unbroken four-dimensional $\lambda\phi^4$ theory, we reproduce the known results at ${1 \ll n \ll \lambda^{-1}}$.