SIMILARITY RENORMALIZATION OF THE ELECTRON-PHONON COUPLING

We study the problem of the phonon-induced electron-electron interacti on in a solid. Starting with a Hamiltonian that contains an electron-p honon interaction, we perform a similarity renormalization transformat ion to calculate an effective Hamiltonian. Using this transformation s ingularities due to degeneracies are avoided explicitly. The effective interactions are calculated to second order in the electron-phonon co upling. It is shown that the effective interaction between two electro ns forming a Cooper pair is attractive in the whole parameter space. F or a simple Einstein model we calculate the renormalization of the ele ctronic energies and the critical temperature of superconductivity.