Adiabatic Approximations and Superconductivity Theories

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Abstract
In a number of recent suggestions for a theory of superconductivity a variant of the conventional perturbation theory was used to treat the lattice-electron interaction in crystals and to obtain apparently new results which were different from the theory proposed earlier by Fröhlich. It is demonstrated here that the variant theory, which uses the same matrix elements as Fröhlich, gives identically the same correction to the energy of the crystal as does the Fröhlich theory and that the apparently new results stem from erroneous neglect of the renormalization of the sound frequencies and of the zero-point motion.