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

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.