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

TL;DR

This paper establishes Hardy-Dirac inequalities with various weights and uses them to define unique self-adjoint extensions of Dirac operators for specific diagonal potentials, advancing mathematical understanding of quantum operators.

Contribution

It introduces new Hardy-Dirac inequalities with measure-valued and Coulombic weights and applies these to construct distinguished self-adjoint extensions of Dirac operators.

Findings

Established Hardy-Dirac inequalities with measure-valued and Coulombic weights.

Constructed distinguished self-adjoint extensions for Dirac operators with certain diagonal potentials.

Enhanced mathematical framework for analyzing Dirac operators in quantum mechanics.

Abstract

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 above mentioned inequalities.