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 nonhomogeneous magnetic field B = curl A. The following Lieb-Thirring type inequality for the moment of negative eigenvalues is established as [GRAPHICS] where p > 3/2 and b(p)(x) is the L-p average of \B\ over certain cube centered at x 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) 1998 Academic Press.