On perturbations of Dirac operators with variable magnetic field of constant direction

Details On perturbations of Dirac operators with variable magnetic field of constant direction On perturbations of Dirac operators with variable magnetic field of constant direction

2004-05-05

arxiv.org/abs/math-ph/0405013v1

Physics

Mathematical Physics

12 pages

Scientific paper

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.

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