Field theory for the one-dimensional optical polaron. I. Incorporation of the Goldstone mode and interaction with internal phonons

An interacting electron-phonon field theory is developed for the one-dimensional Holstein molecular-crystal polaron. The Goldstone mode must be separated from the internal phonons and treated to all orders in its amplitude. A systematic perturbation scheme for the renormalized phonons is outlined. Kinematic corrections to the adiabatic polaron binding energy and effective mass are obtained.