A scaling approach to locally coupled electron-phonon systems

The authors give a brief outline of a 'poor man's' scaling approach as applied to locally coupled electron-phonon systems. For these systems they show that the retardation of the effective interactions have to be taken into account. The approach is extended to the calculation of one-electron Green functions and applied to the spinless Anderson model coupled to phonons. A general expression is obtained for the renormalisation of the resonance width due to phonons. This gives the results of Hewson and Newns (1979, 1980) in the appropriate limits but is more general in being applicable to a continuum spectrum of local phonons and for all values of the coupling strength.