Sharp Lieb-Thirring inequalities in high dimensions

Abstract

We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schrodinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$ with $\gamma\ge 3/2$ and arbitrary $d\ge 1$. (revised, to appear in Acta Math)