## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 45, Number 2 (2016), 263-270.

### 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 decays suitably at infinity. We show that the the zero resonance is absent for $H$, extending recent results of Sait\={o}-Umeda [6] and Zhong-Gao [7].

#### Article information

**Source**

Hokkaido Math. J., Volume 45, Number 2 (2016), 263-270.

**Dates**

First available in Project Euclid: 2 August 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1470139404

**Digital Object Identifier**

doi:10.14492/hokmj/1470139404

**Mathematical Reviews number (MathSciNet)**

MR3532132

**Zentralblatt MATH identifier**

1342.35275

**Subjects**

Primary: 35P99: None of the above, but in this section 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

**Keywords**

Dirac operators zero resonances

#### Citation

AIBA, Daisuke. Absence of zero resonances of massless Dirac operators. Hokkaido Math. J. 45 (2016), no. 2, 263--270. doi:10.14492/hokmj/1470139404. https://projecteuclid.org/euclid.hokmj/1470139404