  We comment on the discretization of the Dirac equation using finite element
spaces of differential forms. In order to treat perturbations by low order
terms, such as those arizing from electromagnetic fields, we develop some
abstract discretization theory and provide estimates in fractional order
Sobolev spaces for finite element systems. Eigenmode convergence is proved, as
well as optimal convergence orders, assuming a flat background metric on a
periodic domain.
