On Moments of Negative Eigenvalues for the Pauli Operator

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