| Contrary to theories of spin fluctuations in strongly correlated systems which are ill defined and in most cases suffer on arbitrariness, the theory of the electron-phonon interaction in strongly correlated systems can be formulated in a consistent and controllable way. Accordingly, I will discuss the theory of strongly correlated systems (with large on-site repulsion) which predicts in a controllable way that the effective interaction between charges is non-local and long-ranged. The most important example is the appearance of the forward scattering peak (FSP) in the electron-phonon interaction (EPI) and in the scattering potential of nonmagnetic impurities. FSP is due to the suppression of doubly occupancy and is accounted for by the three- and four-points vertex functions and can not be described by the present version of the dynamical mean-field theory (DMFT). For the first time both ionic and covalent contribution to EPI in strongly correlated systems will be discussed and applied to HTSC materials and heavy fermions. It will be argued that the existence of FSP in EPI of HTSC materials is inevitable fact which favours d-wave pairing and robustness of these superconductors in the presence of nonmagnetic impurities and defects. The similar situation holds in other strongly correlated systems such as heavy fermions. I will also discuss and formulate the correct theory for the phonon-spectra in strongly correlated systems, which goes far beyond the unfounded and uncritically used Fröhlich model. |
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