Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectral properties of Dirac operators with electrostatic
  $\delta$-shell interactions   In this paper the spectral properties of Dirac operators $A_\eta$ with
electrostatic $\delta$-shell interactions of constant strength $\eta$ supported
on compact smooth surfaces in $\mathbb{R}^3$ are studied. Making use of
boundary triple techniques a Krein type resolvent formula and a
Birman-Schwinger principle are obtained. With the help of these tools some
spectral, scattering, and asymptotic properties of $A_\eta$ are investigated.
In particular, it turns out that the discrete spectrum of $A_\eta$ inside the
gap of the essential spectrum is finite, the difference of the third powers of
the resolvents of $A_\eta$ and the free Dirac operator $A_0$ is trace class,
and in the nonrelativistic limit $A_\eta$ converges in the norm resolvent sense
to a Schr\"odinger operator with an electric $\delta$-potential of strength
$\eta$.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: eess