Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The zero modes and zero resonances of massless Dirac operators   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 < x >^{-\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 $\rho > 3/2$.

0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat