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arXiv · 1810.01659

Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations

Biagio Cassano·Fabio Pizzichillo
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Abstract

We determine explicitly a boundary triple for the Dirac operator $H:=-iα\cdot \nabla + mβ+ \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= |x|^{-1} ( ν\mathbb{I}_4 +μβ-i λα\cdot{x}/|x|\,β)$, with $ν,μ,λ\in \mathbb R$. Consequently we determine all the self-adjoint realizations of $H$ in terms of the behaviour of the functions of their domain in the origin. When $\sup_{x} |x||\mathbb V(x)| \leq 1$, we discuss the problem of selecting the distinguished extension requiring that its domain is included in the domain of the appropriate quadratic form.

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Biagio Cassano, Fabio Pizzichillo. 2019-04-05. Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations. https://doi.org/10.1063/1.5063986

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