On moments of negative eigenvalues for the Pauli operator

This paper concerns the three-dimensional Pauli operator P = (sigma . (p - A(x)))(2) + V(x) with a non-homogeneous magnetic field B = curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established, [GRAPHICS] where p > 3/2 and b(p)(x) is the L-p average of \B\ over a certain cube centered at s with a side length scaling like \B\(-1/2). We also show that, if B has a constant direction, [GRAPHICS] where gamma > 1/2 and p > 1. (C) 1999 Academic Press.