Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjointness of the 2D Dirac operator with singular interactions
  supported on star-graphs   We consider the two-dimensional Dirac operator with Lorentz-scalar
$\delta$-shell interactions on each edge of a star-graph. An orthogonal
decomposition is performed which shows such an operator is unitarily equivalent
to an orthogonal sum of half-line Dirac operators with off-diagonal Coulomb
potentials. This decomposition reduces the computation of the deficiency
indices to determining the number of eigenvalues of a one-dimensional
spin-orbit operator in the interval $(-1/2,1/2)$.
  If the number of edges of the star graph is two or three, these deficiency
indices can then be analytically determined for a range of parameters. For
higher numbers of edges, it is possible to numerically calculate the deficiency
indices. Among others, examples are given where the strength of the
Lorentz-scalar interactions directly change the deficiency indices while other
parameters are all fixed and where the deficiency indices are $(2,2)$, neither
of which have been observed in the literature to the best knowledge of the
authors. For those Dirac operators which are not already self-adjoint and do
not have $0$ in the spectrum of the associated spin-orbit operator, the
distinguished self-adjoint extension is also characterized.

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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: ao-sci