Non-perturbative analysis of the infrared properties of QED3

We analyse the Dyson-Schwinger equations of the photon and electron propagator of massless QED3. Although the perturbation expansion in this theory contains infrared divergences, the Dyson-Schwinger equations admit well-defined solutions. Perturbative infrared divergences are replaced, in the solutions of the Dyson-Schwinger equations, by new parameters, which are matrix elements of field operators. The full electron propagator is shown to depend crucially on the effective photon mass 〈AμAμ〉.We point out the relevance of our approach to the analysis of Dyson-Scwinger equations in other theories.