On Moments of Negative Eigenvalues for the Pauli Operator

This paper concerns the three-dimensional Pauli operator with a non-homogeneous magnetic fieldB=curl A. The following Lieb–Thirring type inequality for the moment of negative eigenvalues is established, wherep>3/2 andbp(x) is theLpaverage of B over a certain cube centered atxwith a side length scaling like B−1/2. We also show that, ifBhas a constant direction, whereγ>1/2 and p>1.