Remark on essential selfadjointness of Dirac operators with Coulomb potentials (Q1821969)

We study the Dirac operator \(\alpha _ jD_ j+P(x)\) with a multicenter matrix value potential \(P(x)=\sum ^{\infty}_{j=1}P_ j(x-a_ j)\), where each \(P_ j(x)\) is locally bounded by \(\mu _ j| x| ^{- 1}\), \(\mu _ j<3^{1/2}/2\). From the local inequality \(\| r^{- 1}u\| \leq c_{\mu}\| (\alpha _ jD_ j+P)u\|\) at \(x=0\) we infer all informations about essential selfadjointness on \(C_ 0^{\infty}({\mathbb{R}}^ 3\setminus \{a_ 1,a_ 2,...\})^ 4\), domain preserving property and invariance of essential spectrum.