THE LADDER APPROXIMATION IN QED(2)

We study the Schwinger-Dyson equation for the fermion self-energy in m assless and massive QED2, in the ladder approximation. When the fermio n is massless (and the photon massless or massive), we check the relia bility of this approximation by comparing its solutions with the exact ones. They agree only when the photon is massless. For a massive ferm ion and massless photon, we show that there is no consistent solution at all, the infrared divergences introduced by the approximation forbi dding even the trivial solution. When both fermion and photon are mass ive, we find a non-perturbative (extra) fermion mass generation (which survives in the limit when the bare mass of the fermion tends to zero ). We argue that, in this case, the ladder approximation will provide reliable results if the bare masses of the fields are large compared w ith the (dimensionful) coupling constant.