Dynamical breakdown of symmetries in three-dimensional QED

We analyze the possibility of dynamical breakdown of parity in three-dimensional QED. We find that for an even number of fermions only chiral symmetry is broken dynamically while parity is conserved. For an odd number of fermions, where a parity-conserving mass generation is not possible, we find no consistent nontrivial solution for the Schwinger-Dyson equations, leading us to conjecture that at least one fermion remains massless and no mass is induced for the photon in this case.