A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields

Rafael D. Benguria, Hanne Van Den Bosch

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 exis…