Absence of zero resonances of massless Dirac operators

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 $4\times 4$ Hermitian matrix valued function which suitably decays at infinity. We show that the the zero resonance is absent for $H$, extending recent results of Saitō-Umeda and Zhong-Gao.

7pages