Abstract
The Ward identity is derived for the electron-phonon coupling in one dimension and the spectrum of elementary excitations is calculated by assuming that the Fermi distribution is not strongly distorted by the interaction. The electron-phonon vertex is renormalised in the case of the forward scattering and Migdal's theorem (1958) is discussed. A model is proposed for the giant Kohn anomaly. The dip in the phonon spectrum is obtained and compared with the experimental data for KCP.
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