Absence of real resonances of Dirac operators

TL;DR

This paper investigates the resonances of Dirac operators by extending the resolvent meromorphically, establishing their localization, and analyzing specific cases like external fields and the MIT bag model.

Contribution

It introduces the concept of resonances for Dirac operators and proves a Rellich-type theorem for their localization in specific physical models.

Findings

No real resonances are present for the considered Dirac operators.

Resonance localization results are established for external fields and the MIT bag model.

The study extends the understanding of spectral properties of Dirac operators.

Abstract

The purpose of this paper is to introduce the resonances of Dirac operators by continuing meromorphically the truncated resolvent and to establish a result about their localization : a kind of Rellich Theorem. Firstly, we consider the case of the Dirac operator in an external field which is essentially bounded and compactly supported. Secondly, we consider the case of the MIT bag model outside a smooth and bounded obstacle.