Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-3

January 2000

In this paper we describe an intrinsically geometric way of producing magnetic fields on $\S^3$ and $\R^3$ for which the corresponding Dirac operators have a non-trivial kernel. In many cases we are able to compute the dimension of the kernel. In particular we can give examples where the kernel has any given dimension. This generalizes the examples of Loss and Yau (Commun. Math. Phys. 104 (1986) 283-290).

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