Eigenvalues and resonances of Dirac operators with dilation analytic potentials diverging at infinity

Abstract

We study spectra and resonances of Dirac operators with an electric potential diverging at infinity and a bounded magnetic potential with the help of the dilation analytic method and the Foldy-Wouthuysen-Tani transform. After investigating the spectrum, we study on resonance-free regions. We also show that resonances of the Dirac operator exist near eigenvalues of a Pauli operator or resonances of another Pauli operator when the velocity of light $c$ is sufficiently large.