  A many-body coherent potential approximation (CPA) previously developed for
the double exchange (DE) model is extended to include coupling to local quantum
phonons. The Holstein-DE model studied (equal to the Holstein model for zero
Hund coupling) is considered to be a simple model for the colossal
magnetoresistance manganites. We concentrate on effects due to the quantisation
of the phonons, such as the formation of polaron subbands. The electronic
spectrum and resistivity are investigated for a range of temperature and
electron-phonon coupling strengths. Good agreement with experiment is found for
the Curie temperature and resistivity with intermediate electron-phonon
coupling strength, but phonon quantisation is found not to have a significant
effect in this coupling regime.
