A Test of The Source Galerkin Method

TL;DR

This paper evaluates the Source Galerkin method's effectiveness in solving quantum field theories by applying it to a well-understood zero-dimensional phi^4 model, aiming to demonstrate its potential advantages over traditional methods.

Contribution

The paper presents the first application of the Source Galerkin method to a known quantum field theory model, testing its accuracy and developing techniques for future complex applications.

Findings

SG method successfully reproduces known solutions of phi^4 theory

SG shows potential for faster computations than Monte Carlo methods

Developed techniques for applying SG to more complex theories

Abstract

Some results of the ongoing development of our Source Galerkin (SG) nonperturbative approach to numerically solving Quantum Field theories are presented. This technique has the potential to be much faster than Monte Carlo methods. SG uses known symmetries and theoretical properties of a theory. In order to test this approach, we applied it to phi^4 theory in zero dimensions. This model has been extensively studied and has a known set of exact solutions. This allows us to broaden the understanding of various properties of the SG method and to develop techniques necessary for the successful application of this method to more sophisticated theories.