The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schrödinger
operator in terms of an Lp norm of the potential. This is dual to a bound
on the H1-norms of a system of orthonormal functions.
We extend these to analogous inequalities for perturbations of the Fermi sea of
non-interacting particles, i.e., for perturbations of the continuous spectrum of
the Laplacian by local potentials. (This is joint work with R. Frank, M. Lewin and E. Lieb.)