Flow Equations for Electron-Phonon Interactions

Abstract

A recently 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 Fröhlich-transformations. 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.