- 07-100 Yoshimi Saito, Tomio Umeda
- The zero modes and zero resonances of massless Dirac operators
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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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