Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noninteger flux - why it does not work   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.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an