The properties of a one-dimensional system of degenerate electrons coupled to long-wavelength phonons are investigated. The equivalent model Hamiltonian of Tomonaga, which describes the electrons by density waves, is diagonalized to normal modes. These are calculated for the Einstein model and constant coupling, and used to get the ground-state energy. A physical interpretation of the model is given. The breakdown of the system for strong coupling is discussed. The many-body perturbation theory is used to assess the validity of the Tomonaga model. The electron-phonon ground-state energy diagrams may be grouped in two sets as Tomonaga and non-Tomonaga. The latter cancel among themselves exactly to a high order. The extent of the cancellation in three dimensions is treated in fourth order and found to be significant, but not exact.