  A recently developed renormalization approach is used to study the
electron-phonon coupling in many-electron systems. By starting from an
Hamiltonian which includes a small gauge symmetry breaking field, we directly
derive a BCS-like equation for the energy gap from the renormalization
approach. The effective electron-electron interaction for Cooper pairs does not
contain any singularities. Furthermore, it is found that phonon-induced
particle-hole excitations only contribute to the attractive electron-electron
interaction if their energy difference is smaller than the phonon energy.

Superconductivity