A recently [9] proposed method of continuous unitary transformations is used to eliminate the interaction between electrons and phonons. The differential equations for the couplings represent an infinitesimal formulation of a sequence of Fröhlichtransformations [5]. The two approaches are compared. Our result will turn out to be less singular than Fröhlich’s. Furthermore the interaction between electrons belonging to a Cooper-pair will always be attractive in our approach. Even in the case where Fröhlich’s transformation is not defined (Fröhlich actually excluded these regions from the transformation), we obtain an elimination of the electron-phonon interaction. This is due to a sufficiently slow change of the phonon energies as a function of the flow parameter. 1 New address: Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Kantstraße 55,
A Green function technique is used to study the electron-phonon interaction in the Hubbard model. The Coulomb interaction constant is renormalised owing to the electron-phonon interaction; this renormalisation always produces an increase in the critical temperature T c . The dependence of the electronic damping on the ratio U/W (Coulomb interaction per band width) and on the band occupation n for different temperatures is discussed. The damping gamma (T, U/W) shows different behaviours for U=constant and W=constant.