Absence of eigenvalues 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. Our results can be viewed as a generalization of those obtained by Cossetti, Fanelli and Krej\v{c}i\v{r}\'ik (2020), which treated the purely magnetic case. We also emphasize that, in the massless case, our approach covers Coulomb-type potentials of the form $V(x) = \frac{1}{|x|} \big(\nu \mathbb{I} + \mu \beta + i \delta \beta \big(\boldsymbol{\alpha}\cdot \frac{x}{|x|} \big) \big).$