Absence of embedded eigenvalues of Pauli and Dirac operators

Abstract

We consider eigenvalues of the Pauli operator in ${\mathbb{R}}^3$ embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and electric field at infinity. We show moreover that the decay conditions on the magnetic and electric field are sharp. Analogous results are obtained for purely magnetic Dirac operators.