High-energy Behavior of the Scattering Amplitude for a Dirac Operator

Abstract

We study the high-energy behavior of the scattering amplitude and the total scattering cross section for a Dirac operator with a 4 x 4 matrix-valued potential. Moreover, in the electro-magnetic case, it is shown that the electric potential and the magnetic field can be reconstructed from the high-energy behavior of the scattering amplitude. The study of the high-energy behavior of the resolvent estimates is crucial for our proof.