# The kernel of Dirac operators on S3 and R3

Erdös L. 2000.The kernel of Dirac operators on S3 and R3. In: Differential Equations and Mathematical Physics. AMS/IP Studies in Advanced Mathematics, vol. 16, 111–119.

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AMS/IP Studies in Advanced Mathematics

Abstract

In this paper we describe an intrinsically geometric way of producing magnetic fields on §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).

Publishing Year

Date Published

2000-01-01

Book Title

Differential Equations and Mathematical Physics

Acknowledgement

L. Erdös was supported by the N.S.F. grant DMS-9970323. J. P. Solovej was supported in parts by the EU TMR-grant FMRX-CT 96-0001 by MaPhySto — Centre for Mathematical Physics and Stochastics, funded by a grant from The Danish National Research Foundation and by a grant from the Danish Natural Science Research Council.

Volume

16

Page

111 - 119

ISBN

IST-REx-ID

### Cite this

Erdös L. The kernel of Dirac operators on S3 and R3. In:

*Differential Equations and Mathematical Physics*. Vol 16. American Mathematical Society; 2000:111-119. doi:10.1090/amsip/016Erdös, L. (2000). The kernel of Dirac operators on S3 and R3. In

*Differential Equations and Mathematical Physics*(Vol. 16, pp. 111–119). American Mathematical Society. https://doi.org/10.1090/amsip/016Erdös, László. “The Kernel of Dirac Operators on S3 and R3.” In

*Differential Equations and Mathematical Physics*, 16:111–19. American Mathematical Society, 2000. https://doi.org/10.1090/amsip/016.L. Erdös, “The kernel of Dirac operators on S3 and R3,” in

*Differential Equations and Mathematical Physics*, vol. 16, American Mathematical Society, 2000, pp. 111–119.Erdös, László. “The Kernel of Dirac Operators on S3 and R3.”

*Differential Equations and Mathematical Physics*, vol. 16, American Mathematical Society, 2000, pp. 111–19, doi:10.1090/amsip/016.### Export

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arXiv math-ph/0001036