Using a new method for the solution of the FLEX-equations, which allows the determination of the self energy $\Sigma_{ \bf k}(\omega)$ of the $2D$ Hubbard model on the real frequency axis, we calculate the doping dependence of the quasi-particle excitations of High-T$_c$ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasi particle dispersion, an anomalous $\omega$-dependence of ${ \rm Im}\Sigma_{ \bf k}(\omega)$ and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.
Categories: cond-mat