Numerical Field Theory on the Continuum

TL;DR

This paper presents a numerical approach based on source Galerkin methods to approximate solutions to continuum Schwinger-Dyson equations, demonstrated with b4^4 in one dimension, highlighting numerical challenges and future prospects.

Contribution

It introduces a numerical method using source Galerkin techniques for solving continuum Schwinger-Dyson equations, with practical examples and discussion of computational issues.

Findings

Successful approximation of b4^4 in D=1

Identification of numerical challenges in the method

Discussion of future computational opportunities

Abstract

An approach to calculating approximate solutions to the continuum Schwinger-Dyson equations is outlined, with examples for \phi^4 in D=1. This approach is based on the source Galerkin methods developed by Garcia, Guralnik and Lawson. Numerical issues and opportunities for future calculations are also discussed briefly.