Nonperturbative Lattice Simulation of High Multiplicity Cross Section Bound in $\phi^4_3$ on Beowulf Supercomputer

TL;DR

This paper uses Monte Carlo simulations on a Beowulf supercomputer to investigate high multiplicity cross sections in three-dimensional $$ $$ theory, finding no evidence of large cross sections where perturbative estimates predicted them.

Contribution

It introduces a nonperturbative lattice simulation approach to study high multiplicity cross sections in $$ $$ theory and compares results with perturbative predictions.

Findings

No evidence of large cross sections in the simulated range.

Simulation results align with perturbation theory predictions.

Spectral sum rules provide bounds on cross sections.

Abstract

In this thesis, we have investigated the possibility of large cross sections at large multiplicity in weakly coupled three dimensional $\phi^4$ theory using Monte Carlo Simulation methods. We have built a Beowulf Supercomputer for this purpose. We use spectral function sum rules to derive a bound on the total cross section where the quantity determining the bound can be measured by Monte Carlo simulation in Euclidean space. We determine the critical threshold energy for large high multiplicity cross section according to the analysis of M.B. Volosion and E.N. Argyres, R.M.P. Kleiss, and C.G. Papadopoulos. We compare the simulation results with the perturbation results and see no evidence for large cross section in the range where tree diagram estimates suggest they should exist.