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 ei genvalues is established as [GRAPHICS] where p > 3/2 and b(p)(x) is th e L-p average of \B\ over certain cube centered at x with a side lengt h scaling like \B\(-1/2). We also show that, if B has a constant direc tion. [GRAPHICS] where gamma>1/2 and p>1. (C) 1998 Academic Press.