On the spectrum of the magnetic Dirac operator

2025/12/15 by Branding, Volker, Ginoux, Nicolas, Habib, Georges · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.2512.13338

openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28

Abstract

The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this article is a first step towards filling this gap. To this end we provide a number of eigenvalue estimates for the magnetic Dirac operator on closed Riemannian manifolds and explicitly compute its spectrum for specific choices of the magnetic field on the flat torus and on the three-dimensional round sphere.

Citations

• A note on the existence of nontrivial zero modes on Riemannian manifolds
• Which magnetic fields support a zero mode?
• Rigidity results for Riemannian spin^c manifolds with foliated boundary
• Geometric aspects of transversal Killing spinors on Riemannian flows
• Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinors

Cited by

• Conformal invariants for the zero mode equation

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