  The effective action for Q.E.D in external magnetic field is constructed
using the method of inhomogeneity expansion. We first treat the
non-relativistic case where a Chern-Simons like term is generated. We then
consider the full relativistic theory and derive the effective action for the
$A_{\mu}$ fields.
  In the non-relativistic case we also add a 4-fermi type interaction and show
that under certain circumstances, it corresponds to a Zeeman type term in the
effective action.
