07-100 Yoshimi Saito, Tomio Umeda
The zero modes and zero resonances of massless Dirac operators (71K, LaTeX2e) Apr 24, 07
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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 ,} nabla_x$, and $Q(x)= big( q_{jk} (x) big)$ 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 $ rho > 3/2$.

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