Dynamical symmetry breaking in planar QED

We investigate (2 + 1)-dimensional QED coupled with Dirac fermions both at zero and finite temperature. We discuss in detail two-component (P-odd) and four-component (P-even) fermion fields. We focus on P-odd and P-even Dirac fermions in the presence of an external constant magnetic field. In the one-loop approximation we find that the spontaneous generation of a uniform magnetic condensate is energetically favoured in the case of the P-odd massive theory. Moreover, we find that the spontaneous generation of the magnetic condensate survives even at infinite temperature. We also discuss the spontaneous generation of fermion mass in the presence of an external magnetic field.