Naiara Arrizabalaga

SELF-ADJOINT EXTENSIONS OF DIRAC OPERATORS WITH COULOMB TYPE SINGULARITY

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.

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the mentioned inequalities.

An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators

In this article we investigate spectral properties of the coupling

On the MIT Bag Model in the Non-relativistic Limit

{H + V_\lambda}

Shell Interactions for Dirac Operators

H+Vλ, where

Extension operator for the MIT bag model

{H = -i\alpha \cdot \nabla+m\beta}