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Peer-reviewedCC BY 4.0Annales Henri Poincaré

On the spectrum of the magnetic Dirac operator

  • Volker Branding
  • Nicolas Ginoux
  • Georges Habib
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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.

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Cite

BibTeXRIS
BibTeX
@article{branding2026spectrum,
  title = {{On the spectrum of the magnetic Dirac operator}},
  author = {Volker Branding and Nicolas Ginoux and Georges Habib},
  journal = {Annales Henri Poincaré},
  year = {2026},
  month = nov,
  doi = {10.1007/s00023-026-01778-w},
  url = {https://hal.science/hal-05415814v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On the spectrum of the magnetic Dirac operator
AU  - Volker Branding
AU  - Nicolas Ginoux
AU  - Georges Habib
PY  - 2026
DA  - 2026/11/03
JO  - Annales Henri Poincaré
DO  - 10.1007/s00023-026-01778-w
UR  - https://hal.science/hal-05415814v2
AB  - 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.
SN  - 1424-0637
SN  - 1424-0661
ER  -