ELECTRON-PHONON INTERACTION IN ONE-DIMENSION - EXACT SPECTRAL PROPERTIES

One-electron spectral functions for a one-dimensional continuum model including electron-phonon coupling are calculated exactly. The electro ns coupled to the phonons represent a Luttinger liquid. Results are pr esented for an Einstein model for spinless electrons and for the model including spin. Apart from Luttinger-liquid features, the spectra sho w a rich satellite structure with peak separations partially determine d by matrix-element effects. The use of Migdal's approximation neglect ing vertex corrections fails to reproduce the exact spectra even for a n effective bandwidth large compared to the phonon frequency. The rele vance to high-resolution valence photoemission from quasi-one-dimensio nal conductors is discussed.