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

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.