Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dirac operators, shell interactions and discontinuous gauge functions
  across the boundary   Given a bounded smooth domain $\Omega\subset\mathbb{R}^3$, we explore the
relation between couplings of the free Dirac operator
$-i\alpha\cdot\nabla+m\beta$ with pure electrostatic shell potentials
$\lambda\delta_{\partial\Omega}$ ($\lambda\in\mathbb{R}$) and some
perturbations of those potentials given by the normal vector field $N$ on the
shell $\partial\Omega$, namely $\{\lambda_e+\lambda_n(\alpha\cdot
N)\}\delta_{\partial\Omega}$ ($\lambda_e$, $\lambda_n\in\mathbb{R}$). Under the
appropiate change of parameters, the couplings with perturbed and unperturbed
electrostatic shell potentials yield unitary equivalent self-adjoint operators.
The proof relies on the construction of an explicit family of unitary operators
that is well adapted to the study of shell interactions, and fits within the
framework of gauge theory. A generalization of such unitary operators also
allow us to deal with the self-adjointness of couplings of
$-i\alpha\cdot\nabla+m\beta$ with some shell potentials of magnetic type,
namely $\lambda(\alpha\cdot N)\delta_{\partial\Omega}$ with $\lambda\in
C^1(\partial\Omega)$.

10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th