On the point spectrum of electromagnetic Dirac operators

Abstract

In this work, we develop the method of multipliers for electromagnetic Dirac operators and establish sufficient conditions on the magnetic and electric fields that guarantee the absence of point spectrum. In the massless case, our approach covers Coulomb-type potentials of the form $V(x) = \frac{1}{|x|} \big(\nu \mathbb{I} + \mu \beta + i \delta \beta \big(\boldsymbol{\alpha}\cdot \frac{x}{|x|} \big) \big).$ We also adapt the method to show absence of embedded eigenvalues above a threshold which depends on the asymptotic behaviour of the magnetic and electric fields.