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May 2008 The zero modes and zero resonances of massless Dirac operators
Yoshimi SAITŌ, Tomio UMEDA
Hokkaido Math. J. 37(2): 363-388 (May 2008). DOI: 10.14492/hokmj/1253539560

Abstract

The zero modes and zero resonances of the Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \, \alpha_2, \, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $D=\frac{1}{i} ∇_x$, and $Q(x)=( q_{jk} (x))$ is a $4\times 4$ Hermitian matrix-valued function with $| q_{jk}(x) | \le C \langle x \rangle^{-\rho}$, $\rho >1$. We shall show that every zero mode $f(x)$ is continuous on ${\mathbb R}^3$ and decays at infinity with the decay rate $|x|^{-2}$. Also, we shall show that $H$ has no zero resonance if $ρ > 3/2$.

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Yoshimi SAITŌ. Tomio UMEDA. "The zero modes and zero resonances of massless Dirac operators." Hokkaido Math. J. 37 (2) 363 - 388, May 2008. https://doi.org/10.14492/hokmj/1253539560

Information

Published: May 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1144.35458
MathSciNet: MR2415906
Digital Object Identifier: 10.14492/hokmj/1253539560

Subjects:
Primary: 35Q40
Secondary: 35P99, 81Q10

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 2 • May 2008
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