Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 102, 12 pages      arXiv:2306.00590      https://doi.org/10.3842/SIGMA.2023.102
Contribution to the Special Issue on Global Analysis on Manifolds in honor of Christian Bär for his 60th birthday

A Note on the Spectrum of Magnetic Dirac Operators

Nelia Charalambous a and Nadine Große b
a) Department of Mathematics and Statistics, University of Cyprus, Nicosia, 1678, Cyprus
b) Mathematisches Institut, Universität Freiburg, 79100 Freiburg, Germany

Received June 02, 2023, in final form December 14, 2023; Published online December 22, 2023

Abstract
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the spectrum is either maximal, or discrete. We also show that magnetic Dirac operators can have a dense set of eigenvalues.

Key words: Dirac operator; potentials; spectrum.

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