Microscopic derivation of the role of phonon-mediated electron-electron interactions in the low-temperature resistivity of metals

A microscopic justification is given of MacDonald's suggestion (1980, 1981) that an important source of the low-temperature resistivity of simple metals is an effective inter-electron interaction mediated by virtual phonons. It is shown that Migdal's theorem (1951) require restatement to deal with the low-temperature regime correctly.