Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations

TL;DR

This paper reviews modern numerical methods for solving Dyson-Schwinger and Bethe-Salpeter equations, focusing on meson and baryon construction, form-factor calculations, and remaining challenges in bound-state physics.

Contribution

It provides a comprehensive overview of algorithms and techniques for bound-state calculations, including extensions beyond the rainbow-ladder truncation.

Findings

Effective algorithms for meson and baryon construction

Self-consistent calculation of form-factors demonstrated

Discussion of challenges in bound-state calculations

Abstract

We review in detail modern numerical methods used in the determination and solution of Bethe-Salpeter and Dyson--Schwinger equations. The algorithms and techniques described are applicable to both the rainbow-ladder truncation and its non-trivial extensions. We discuss pedagogically the steps involved in constructing conventional mesons and baryons as systems of two- and three-quarks respectively. As further application we describe the self-consistent calculation of form-factors and highlight the challenges that remain therein.