Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory

TL;DR

This paper introduces the Source Galerkin method for solving quantum field theories and proposes a novel perturbation theory approach using Sinc function expansions, enhancing computational efficiency and applicability.

Contribution

It develops the Source Galerkin method for higher-dimensional field theories and introduces Sinc-based perturbation calculations, offering new computational tools.

Findings

Effective approximation of Green's functions spectral representations.

Application of the method to scalar and fermionic field theories.

Enhanced computational techniques for quantum field theory solutions.

Abstract

The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green's functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not only possible to apply the Source Galerkin method to higher dimensional field theories, but also leads to a new approach to perturbation theory calculations in scalar and fermionic field theories. This report summarizes the methodologies for solving quantum field theories with the Source Galerkin method and for performing perturbation theory calculations using Sinc approximations.