---
_id: '2710'
abstract:
- lang: eng
  text: 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).
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.
alternative_title:
- AMS/IP Studies in Advanced Mathematics
article_processing_charge: No
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: 'Erdös L. The kernel of Dirac operators on S3 and R3. In: <i>Differential Equations
    and Mathematical Physics</i>. Vol 16. American Mathematical Society; 2000:111-119.
    doi:<a href="https://doi.org/10.1090/amsip/016">10.1090/amsip/016</a>'
  apa: Erdös, L. (2000). The kernel of Dirac operators on S3 and R3. In <i>Differential
    Equations and Mathematical Physics</i> (Vol. 16, pp. 111–119). American Mathematical
    Society. <a href="https://doi.org/10.1090/amsip/016">https://doi.org/10.1090/amsip/016</a>
  chicago: Erdös, László. “The Kernel of Dirac Operators on S3 and R3.” In <i>Differential
    Equations and Mathematical Physics</i>, 16:111–19. American Mathematical Society,
    2000. <a href="https://doi.org/10.1090/amsip/016">https://doi.org/10.1090/amsip/016</a>.
  ieee: L. Erdös, “The kernel of Dirac operators on S3 and R3,” in <i>Differential
    Equations and Mathematical Physics</i>, vol. 16, American Mathematical Society,
    2000, pp. 111–119.
  ista: '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.'
  mla: Erdös, László. “The Kernel of Dirac Operators on S3 and R3.” <i>Differential
    Equations and Mathematical Physics</i>, vol. 16, American Mathematical Society,
    2000, pp. 111–19, doi:<a href="https://doi.org/10.1090/amsip/016">10.1090/amsip/016</a>.
  short: L. Erdös, in:, Differential Equations and Mathematical Physics, American
    Mathematical Society, 2000, pp. 111–119.
date_created: 2018-12-11T11:59:12Z
date_published: 2000-01-01T00:00:00Z
date_updated: 2023-05-03T09:37:03Z
day: '01'
doi: 10.1090/amsip/016
extern: '1'
external_id:
  arxiv:
  - math-ph/0001036
intvolume: '        16'
language:
- iso: eng
month: '01'
oa_version: Preprint
page: 111 - 119
publication: Differential Equations and Mathematical Physics
publication_identifier:
  isbn:
  - '9780821821572'
publication_status: published
publisher: American Mathematical Society
publist_id: '4186'
quality_controlled: '1'
status: public
title: The kernel of Dirac operators on S3 and R3
type: book_chapter
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 16
year: '2000'
...