Hokkaido Mathematical Journal

Absence of zero resonances of massless Dirac operators

Daisuke AIBA

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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

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

First available in Project Euclid: 2 August 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Dirac operators zero resonances


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

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