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In this work we construct self-adjoint extensions of the Dirac operatorassociated to Hermitian matrix potentials with Coulomb decay and prove that thedomain is maximal. The result is obtained by means of a Hardy-Dirac typeinequality. In particular, we can work with some electromagnetic potentialssuch that both, the electric potential and the magnetic one, have Coulomb typesingularity.

Self-adjoint extensions of Dirac operators with Coulomb type singularity