A.A. Balinsky and W.D. Evans
On the zero modes of Pauli operators
(209K, Postscript)

ABSTRACT.  Two results are proved for $\mathrm{nul} \ 
\mathbb{P}_A$, the dimension of the kernel of the Pauli operator 
$\mathbb{P}_A = \bigl\{ \bbf{\sigma} \cdotp \bigl(\frac{1}{i} 
\bbf{\nabla} + \vec{A} \bigr) \bigr\} ^2 $ in $[L^2 
(\mathbb{R}^3)]^2$: 
(i) for $|\vec{B}| \in L^{3/2} 
(\mathbb{R}^3),$ where $\vec{B} = \mathrm{curl} \vec{A}$ is the 
magnetic field, $\mathrm{nul} \ 
\mathbb{P}_{tA} = 0$ except for a finite number of values of $t$ in any 
compact subset of $(0, \infty)$; 
(ii) \ $\bigl\{ \ \vec{B}: \ \mathrm{nul} \ \mathbb{P}_{ A} = 0, 
\ \ | \vec{B} | \in L^{3/2}(\mathbb{R}^3) 
\ \bigr\} $ contains an open dense subset of 
$[L^{3/2}(\mathbb{R}^3)]^3$.