Apparent Electron-Phonon Interaction in Strongly Correlated Systems

We study the interaction of electrons with phonons in strongly correlated solids, having high-T(c) cuprates in mind. Using sum rules, we show that the apparent strength of this interaction strongly depends on the property studied. If the solid has a small fraction (doping) delta of charge carriers, the influence of the interaction on the phonon self-energy is reduced by a factor delta, while there is no corresponding reduction of the coupling seen in the electron self-energy. This supports the interpretation of recent photoemission experiments, assuming a strong coupling to phonons.