Absence of zero resonances of massless Dirac operators

TL;DR

This paper proves that massless Dirac operators in three dimensions do not have zero resonances when the potential decays suitably, extending recent mathematical results in spectral theory.

Contribution

It establishes the absence of zero resonances for massless Dirac operators with decaying potentials, generalizing previous findings by Sait ext={o}-Umeda and Zhong-Gao.

Findings

Zero resonance is absent for the considered Dirac operator.

The result extends previous work to more general potentials.

Provides mathematical conditions ensuring no zero resonance.

Abstract

We consider the massless Dirac operator $H=\alpha \cdot D+Q(x)$ on the Hilbert space $L^{2}(\mathbb{R}^{3},\mathbb{C}^{4})$, where $Q(x)$ is a $4\times4$ Hermitian matrix valued function which suitably decays at infinity. We show that the the zero resonance is absent for $H$, extending recent results of Sait\={o}-Umeda and Zhong-Gao.