07-183 Yoshimi Saito, Tomio Umeda

The asymptotic limits of zero modes of massless Dirac operators (28K, LaTeX 2e) Jul 20, 07

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Abstract. Asymptotic behaviors of zero modes of the massless 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 for every zero mode $f$, the asymptotic limit of $|x|^2f(x)$ as $|x| \to +\infty$ exists. The limit is expressed in terms of an integral of $Q(x)f(x)$.

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