%0 Journal Article
%T A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields
%A Rafael D. Benguria
%A Hanne Van Den Bosch
%J Physics
%D 2015
%I arXiv
%R 10.1063/1.4920924
%X We consider the Pauli operator in $\mathbb R^3$ for magnetic fields in $L^{3/2}$ that decay at infinity as $|x|^{-2-\beta}$ with $\beta > 0$. In this case we are able to prove that the existence of a zero mode for this operator is equivalent to a quantity $\delta(\mathbf B)$, defined below, being equal to zero. Complementing a result from [Balinsky, Evans, Lewis (2001)], this implies that for the class of magnetic fields considered, Sobolev, Hardy and CLR inequalities hold whenever the magnetic field has no zero mode.
%U http://arxiv.org/abs/1503.04470v1