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This 2011 paper **by S.K. Argyropoulos** contains an overview of the non-perturbative formulation of QED in the Schwinger-Dyson formalism.

''For the sake of brevity we have chosen to omit most of the technical details and proofs and concentrate on the physical aspects and applications of the SDE. The avid reader is referred to the original work [1] and references therein. The note is organized as follows. In the first section, we formulate the Schwinger-Dyson equations and derive a closed system of integral equations relating the dynamical fermion mass to the renormalization functions of the photon and fermion fields. The second section contains a brief discussion of critical phenomena and the renormalizaiton group. Finally, we present how this formalism can be used to study critical phenomena in QFT. More precisely we study the chiral transition in strong QED in 4 dimensions and discuss a series of phenomena that arise in the supercritical phase such as dynamical mass generation, vacuum stabilization and dimensional transmutation.''