Letters in Mathematical Physics

, Volume 85, Issue 2–3, pp 111–128 | Cite as

Zero Modes for the Magnetic Pauli Operator in Even-Dimensional Euclidean Space



We study the ground state of the Pauli Hamiltonian with a magnetic field in \({\mathbb{R}^{2d}}\) , d > 1. We consider the case where a scalar potential W is present and the magnetic field B is given by \({B=2i\partial\bar{\partial} W}\) . The main result is that there are no zero modes if the magnetic field decays faster than quadratically at infinity. If the magnetic field decays quadratically then zero modes may appear, and we give a lower bound for the number of them. The results in this paper partly correct a mistake in a paper from 1993.

Mathematics Subject Classification (2000)

Primary: 81Q05 Secondary: 35Q40 47F05 


even-dimensional Dirac and Pauli operators magnetic fields zero-modes 


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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesChalmers University of Technology, Göteborg UniversityGöteborgSweden

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