The asymptotic limits of zero modes of massless Dirac operators

Details The asymptotic limits of zero modes of massless Dirac operators The asymptotic limits of zero modes of massless Dirac operators

2007-07-20

arxiv.org/abs/0707.3008v1

Mathematics

Spectral Theory

9 pages

Scientific paper

10.1007/s11005-007-0207-6

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 < x >^{-\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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