Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials

We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$,for$m\in\mathbb R $,and$\mathbb V(x)= |x|^{-1} ( \nu $\mathbb{I}$_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|},\beta)$,for$\nu,\mu,\lambda \in \mathbb R$. We characterize the self-adjointness in terms of the behaviour of the functions of the domain in the origin, exploiting Hardy-type estimates and trace lemmas. Finally, we describe the distinguished extension.