  Investigating properties of two-dimensional Dirac operators coupled to an
electric and a magnetic field (perpendicular to the plane) requires in general
unbounded (vector-) potentials. If the system has a certain symmetry, the
fields can be described by one-dimensional potentials $V$ and $A$. Assuming
that $|A|<|V|$ outside some arbitrary large ball, we show that absolutely
continuous states of the effective Dirac operators spread ballistically. These
results are based on well-known methods in spectral dynamics together with
certain new Hilbert-Schmidt bounds. We use Lorentz boosts to derive these new
estimates.
