On the spectrum of magnetic Dirac operators with Coulomb-type perturbations

TL;DR

This paper analyzes the spectral properties of 3D Dirac operators with magnetic fields and Coulomb perturbations, establishing the absence of singular continuous spectrum and describing the point spectrum under various magnetic field configurations.

Contribution

It provides new spectral analysis results for Dirac operators with variable magnetic fields and Coulomb-type perturbations, including the limiting absorption principle and spectrum properties.

Findings

Established limiting absorption principle for the operators.

Proved absence of singular continuous spectrum in certain intervals.

Characterized the point spectrum and its properties.

Abstract

We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the perturbations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Constant, periodic as well as diverging magnetic fields are covered, and Coulomb potentials up to the physical nuclear charge Z<137 are allowed. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.