  Using the Hubbard Hamiltonian we analyze the energy- and momentum-dependence
of the elementary excitations in high-T$_c$ superconductors resulting from the
coupling to spin fluctuations. As a result of the energy dependence of the
self-energy $\Sigma ({\bf k}, \omega)$, characteristic features occur in the
spectral density explaining the 'kink' in recent ARPES experiments. We present
results for the spectral density $A({\bf k}, \omega)$ resulting from the
crossover from Im $\Sigma ({\bf k}, \omega)\propto \omega$ to Im $\Sigma ({\bf
k}, \omega)\propto \omega^2$, for the feedback of superconductivity on the
excitations, and for the superconducting order parameter $\Delta({\bf k},
\omega)$. These results relate also to inelastic neutron scattering and
tunneling experiments and shed important light on the essential ingredients a
theory of the elementary excitations in the cuprates must contain.

Superconductivity