Self-Adjoint Extensions of the Dirac Hamiltonian with a delta-Sphere Interaction

TL;DR

This paper explicitly constructs self-adjoint extensions of the Dirac Hamiltonian with a delta-sphere interaction, providing an exact resolvent kernel and clarifying recent related results in the literature.

Contribution

It offers a detailed construction of self-adjoint extensions for the Dirac operator with delta-sphere interaction, including an explicit resolvent kernel.

Findings

Explicit resolvent kernel for free Dirac operator

Construction of self-adjoint extensions with delta-sphere interaction

Clarification of recent related results

Abstract

The purpose of this paper is to make an explicit construction of specific self-adjoint extensions of the Dirac Hamiltonian in the presence of a $\delta$-sphere interaction of finite radius. The exact resolvent kernel of the free Dirac operator is given. This specifies related results that have recently appeared in the literature.