Approximation of Dirac operators with confining electrostatic and Lorentz scalar $\delta$-shell potentials

TL;DR

This paper investigates how to approximate Dirac operators with confining electrostatic and Lorentz scalar delta-shell potentials in the norm resolvent sense, focusing on models where particles cannot penetrate the shell.

Contribution

It introduces a method to approximate Dirac operators with delta-shell potentials that confine particles, advancing understanding of boundary conditions in relativistic quantum models.

Findings

Established norm resolvent convergence of approximations

Demonstrated impermeability of the delta-shell potentials

Provided a rigorous mathematical framework for confining potentials

Abstract

In this paper we study the approximation of Dirac operators with $\delta$-shell potentials in the norm resolvent sense. In particular, we consider the approximation of Dirac operators with confining electrostatic and Lorentz scalar $\delta$-shell potentials, where the support of the $\delta$-shell potentials is impermeable to particles modelled by such Dirac operators.