Non - linear Dynamics in QED 3 and Non - trivial Infrared Structure

In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated consistently. The non-linearity of the equations gives rise to highly non-trivial constraints among the mass and effective (‘running’) gauge coupling, which impose lower and upper bounds on the latter for dynamical mass generation to occur. Possible implications of this to the theory of high-temperature superconductivity are briefly discussed. CERN-TH/99-94 April 1999