New Numerical Methods for Iterative or Perturbative Solution of Quantum Field Theory

TL;DR

This paper introduces a novel numerical approach for solving continuum quantum field theories using lattice source Galerkin methods, enabling high-order perturbative calculations and improved treatment of fermions and bosons.

Contribution

It presents a new computational framework based on lattice source Galerkin methods for continuum quantum field theories, with applications to high-order perturbation theory.

Findings

Method treats fermions and bosons symmetrically.

Enables high-order perturbative graph evaluations.

Offers promising features for quantum field theory computations.

Abstract

A new computational idea for continuum quantum field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spinoff of the technology developed for ``exact'' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order.