Work

On the Spectrum of the Magnetic Dirac Operator

Year: 2026

Type: article

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. This article constitutes a step toward 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.

Source: Annales Henri Poincaré

DOI: 10.1007/s00023-026-01778-w

Authors: Volker Branding, Nicolas Ginoux, Georges Habib

Institutions: University of Rostock, Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine, Lebanese University

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Université de Lorraine, Centre National de la Recherche Scientifique