On the point spectrum of electromagnetic Dirac operators

2025/09/03 by Naiara Arrizabalaga, Arrizabalaga, Naiara, Lucrezia Cossetti +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.03627

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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) = (1)/(|x|) (ν\mathbbI + μβ+ i δβ(\boldsymbolα⋅ (x)/(|x|) ) ). 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.

Citations

• The virial theorem and the method of multipliers in spectral theory
• Absence of embedded eigenvalues of Pauli and Dirac operators
• Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
• A sharp criterion for zero modes of the Dirac equation
• Which magnetic fields support a zero mode?
• Absence of positive eigenvalues of magnetic Schrödinger operators
• On the spectrum of magnetic Dirac operators with Coulomb-type perturbations
• On the zero modes of Pauli operators
• Solution of the Dirac Equation for Scalar Potentials and its Implications in Atomic Physics

Related

• On the spectrum of magnetic Dirac operators with Coulomb-type perturbations
• Absence of embedded eigenvalues of Pauli and Dirac operators
• Magnetic Dirac operator in strips submitted to strong magnetic fields
• A criterion for the existence of non-real eigenvalues for a Dirac operator
• On the spectrum of the magnetic Dirac operator