Masses from nothing. A non-perturbative study of QED3

The dynamical generation of fermion masses is studied in three-dimensional QED as a function of the number of fermion flavours, N. Non-perturbative solutions of the Schwinger-Dyson equation for the full fermion propagator in the Landau gauge are obtained numerically. These are found to exhibit chiral symmetry breaking for all values of N, with no hint of any critical behaviour. The dynamically generated fermion mass and the corresponding condensate are orders of magnitude smaller than the intrinsic scale of the theory and exponentially decrease with N. Such behaviour is, of course, not possible in 1/N perturbation theory and illustrates how a hierarchy of scales can naturally arise non-perturbatively in a gauge theory. (orig.)