Yoshimi Saito, Tomio Umeda
The asymptotic limits of zero modes of massless Dirac operators
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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 $Q(x)f(x)$.