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Noninteger flux - why it does not work
Smilga A.V.
Journal of Mathematical Physics 53 (2012) 042103 - http://hal.in2p3.fr/in2p3-00702813
Physique/Physique des Hautes Energies - Théorie
Physique/Physique mathématique
Mathématiques/Physique mathématique
Noninteger flux - why it does not work
A.V. Smilga1
1 :  SUBATECH - Laboratoire SUBATECH Nantes
CNRS : UMR6457 – IN2P3 – Université de Nantes – École Nationale Supérieure des Mines - Nantes
4, rue Alfred Kastler - 44070 Nantes Cedex 03
We consider the Dirac operator on a 2-sphere without one point in the case of non-integer magnetic flux. We show that the spectral problem for the Hamiltonian (the square of Dirac operator) can always be well defined, if including in the Hilbert space only nonsingular on 2-sphere wave functions. However, this Hilbert space is not invariant under the action of the Dirac operator; the action of the latter on some nonsingular states produces singular functions. This breaks explicitly the supersymmetry of the spectrum. In the integer flux case, the supersymmetry can be restored if extending the Hilbert space to include locally regular sections of the corresponding fiber bundle. For non-integer fluxes, such an extention is not possible.

Articles dans des revues avec comité de lecture
Journal of Mathematical Physics (J. Math. Phys.)
Publisher American Institute of Physics (AIP)
ISSN 0022-2488 

10 pages. The final version to be published in Journ. Math. Phys
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