Hardy-Carleman Type Inequalities for Dirac Operators

TL;DR

This paper establishes new Hardy-Carleman inequalities for Dirac operators, including versions involving magnetic fields, using quadratic form techniques, contributing novel tools for analysis in quantum mechanics and PDEs.

Contribution

It introduces new Hardy-Carleman inequalities for Dirac operators, including magnetic field cases, employing direct quadratic form methods, advancing mathematical tools in quantum physics.

Findings

Derived new Hardy-Carleman inequalities for Dirac operators.

Established inequalities involving traditional weight functions.

Extended results to Dirac particles in magnetic fields.

Abstract

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques.