  An extension of the renormalization group method that includes the effect of
retardation for the interactions of a fermion gas is used to re-examine the
quantum and classical properties of Peierls- like states in one dimension. For
models of spinless and spin-1/2 fermions interacting with either intra or
intermolecular phonons the quantum corrections to the Peierls gap at
half-filling are determined at arbitrary phonon frequency. The nature of
quantum-classical transitions is clarified in weak coupling.
