Non-perturbative Aspects of Schwinger-Dyson Equations

Schwinger-Dyson equations (SDEs) provide a natural staring point to study non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge field theories. We briefly review this research in the context of quenched quantum electrodynamics (QED) and discuss the advances made in the gradual improvement of the assumptions employed to solve these equations. We argue that these attempts render the corresponding studies more and more reliable and suitable for their future use in the more realistic cases of unquenched QED, quantum chromodynamics (QCD) and models alternative to the standard model of particle physics.