Self-adjoint extensions of Dirac operators with Coulomb type singularity

TL;DR

This paper constructs maximal self-adjoint extensions of Dirac operators with Coulomb-type singular potentials, using Hardy-Dirac inequalities, applicable to certain electromagnetic potentials with Coulomb singularities.

Contribution

It provides a method to explicitly construct and characterize maximal self-adjoint extensions of Dirac operators with Coulomb singularities, expanding the understanding of their domain and spectral properties.

Findings

Established maximal domain for Dirac operators with Coulomb potentials

Developed Hardy-Dirac inequality for these operators

Applicable to electromagnetic potentials with Coulomb singularities

Abstract

In this work we construct self-adjoint extensions of the Dirac operator associated to Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The result is obtained by means of a Hardy-Dirac type inequality. In particular, we can work with some electromagnetic potentials such that both, the electric potential and the magnetic one, have Coulomb type singularity.