Letters in Mathematical Physics

, Volume 78, Issue 2, pp 139–156 | Cite as

On the Dirac and Pauli Operators with Several Aharonov–Bohm Solenoids

  • Mikael PerssonEmail author


We study the self-adjoint Pauli operators that can be realized as the square of a self-adjoint Dirac operator and correspond to a magnetic field consisting of a finite number of Aharonov–Bohm solenoids and a regular part, and prove an Aharonov–Casher type formula for the number of zero-modes for these operators. We also see that essentially only one of the Pauli operators are spin-flip invariant, and this operator does not have any zero-modes.

Mathematics Subject Classification (2000)

Primary 81Q10 Secondary 35Q40 Secondary 47F05 


Schrödinger operator spectral analysis 


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Copyright information

© Springer 2006

Authors and Affiliations

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

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