Scattering of Dirac particles by electromagnetic fields with small support in two dimensions and effect from scalar potentials

We study the asymptotic behavior of scattering amplitudes for the scattering of Dirac particles in two dimensions when electromagnetic fields with small support shrink to point-like fields. The result is strongly affected by perturbations of scalar potentials and the asymptotic form changes discontinuously at half-integer fluxes of magnetic fields even for small perturbations. The analysis relies on the behavior at low energy of resolvents of magnetic Schrodinger operators with resonance at zero energy. The magnetic scattering of relativistic particles appears in the interaction of cosmic string with matter. We discuss this closely related subject as an application of the obtained results.