  The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a
Schr\"odinger operator in terms of an $L^p$ norm of the potential. This is dual
to a bound on the $H^1$-norms of a system of orthonormal functions. Here 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.
